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In the recent years, significant research interest has been devoted in the modelling and applications of chaotic systems with stable equilibria. In this research study, we propose a new 3-D chaotic system with two stable node-foci equilibria and an unstable saddle-focus equilibrium. We conduct a detailed bifurcation analysis for the new chaotic system with the aid of bifurcation diagrams and Lyapunov exponents. We also show that the new chaotic system has multistability with coexisting attractors. Using MultiSim version 14.1, we design an electronic circuit for the proposed 3-D chaotic system. Finally, as an application, we introduce a voice cryptosystem using the new chaotic system with two stable node-foci equilibrium points and an unstable saddle-focus equilibrium point and its hardware realization on the FPGA platform.

Wireless power transfer (WPT) system consists of at least two weakly mutual coupled resonant circuits which are tuned to be operated at the same resonant frequency. Since the parameters (i.e. coupling coefficient, load resistance, etc.) could be varied, the multiple zero-phase angle (ZPA) frequencies would be occurred. This phenomenon is known as bifurcation. Some literatures avoid the bifurcation due to its instability issues. Additionally, the bifurcation cannot be easily handled by using the simple variable frequency controller. However, it offers main advantage of coupling-independent operation, allowing the constant voltage or current control regardless of variations in coupling coefficients. Typically, the critical coupling coefficient ( $k_{cri}$ ) is primarily employed for bifurcation criterion during operation. Unfortunately, the exact value of $k_{cri}$ is rather difficult to be obtained in the real system. In this paper, the bifurcation identification from magnetic flux distribution is therefore proposed. Thanks to the unique patterns of magnetic flux distribution at the resonant and bifurcation frequencies, the TMR sensors array can be properly installed to detect the bifurcation through the measured magnetic flux density. The simulated studies and results of finite element method (FEM), using COMSOL Multiphysics, are included for verifications. In addition, the proposed method is implemented and validated basing on the 400W Series-Series WPT hardware prototype. The experimental results show that the sensing voltages from TMR sensors can be effectively used for the detection of bifurcation and lateral misalignment position.

To broaden the stability domain of the H-bridge inverter, a control method of the H-bridge inverter combined with PI and improved power reaching law sliding mode control is studied in this paper. To analyze the complex dynamical behavior of this inverter, firstly, the mathematical model of this system is established and numerical simulation of this model is performed. Secondly, the nonlinear dynamical behavior of this inverter is observed by a bifurcation diagram, folding diagram, stroboscopic diagram, time-domain diagram, and spectral diagram. Thirdly, the stability theory of the system is analyzed by applying the fast-varying stability theorem, and the consistency between the theoretical analysis and numerical simulation further proves the mechanism of nonlinear dynamical behavior occurring in this inverter. Finally, the influence of the circuit parameters: input voltage, load inductance, and load resistance on the nonlinear dynamical behavior of the inverter is analyzed. It is shown that this joint control mode can broaden the operating stability domain of the H-bridge inverter, which provides an important theoretical basis for the design and manufacture of the inverter.

The future of deep space exploration requires high levels of reliability in critical subsystems such as the electrical power system. This paper provides an analysis of voltage stability of direct current (DC) microgrids for spacecraft applications. Bifurcation theory is used to determine the behavior of the system and identify the major causes of voltage instability. The analytical results of the bifurcation model are experimentally verified through a series of tests emulating probable operating conditions of the spacecraft. The findings of this paper are applicable to similar classes of islanded (grid forming) DC electric power systems including aerospace vehicles, shipboard systems, and terrestrial microgrids.

Automated detection of retinal structures, such as retinal vessels (RV), the foveal avascular zone (FAZ), and retinal vascular junctions (RVJ), are of great importance for understanding diseases of the eye and clinical decision-making. In this paper, we propose a novel Voting-based Adaptive Feature Fusion multi-task network (VAFF-Net) for joint segmentation, detection, and classification of RV, FAZ, and RVJ in optical coherence tomography angiography (OCTA). A task-specific voting gate module is proposed to adaptively extract and fuse different features for specific tasks at two levels: features at different spatial positions from a single encoder, and features from multiple encoders. In particular, since the complexity of the microvasculature in OCTA images makes simultaneous precise localization and classification of retinal vascular junctions into bifurcation/crossing a challenging task, we specifically design a task head by combining the heatmap regression and grid classification. We take advantage of three different en face angiograms from various retinal layers, rather than following existing methods that use only a single en face. We carry out extensive experiments on three OCTA datasets acquired using different imaging devices, and the results demonstrate that the proposed method performs on the whole better than either the state-of-the-art single-purpose methods or existing multi-task learning solutions. We also demonstrate that our multi-task learning method generalizes across other imaging modalities, such as color fundus photography, and may potentially be used as a general multi-task learning tool. We also construct three datasets for multiple structure detection, and part of these datasets with the source code and evaluation benchmark have been released for public access. [ABSTRACT FROM AUTHOR]

Vessel enhancement (aka vesselness) filters, are part of angiographic image processing for more than twenty years. Their popularity comes from their ability to enhance tubular structures while filtering out other structures, especially as a preliminary step of vessel segmentation. Choosing the right vesselness filter among the many available can be difficult, and their parametrization requires an accurate understanding of their underlying concepts and a genuine expertise. In particular, using default parameters is often not enough to reach satisfactory results on specific data. Currently, only few benchmarks are available to help the users choosing the best filter and its parameters for a given application. In this article, we present a generic framework to compare vesselness filters. We use this framework to compare seven gold standard filters. Our experiments are performed on three public datasets: the hepatic Ircad dataset (CT images), the Bullit dataset (brain MRA images) and the synthetic VascuSynth dataset. We analyse the results of these seven filters both quantitatively and qualitatively. In particular, we assess their performances in key areas: the organ of interest, the whole vascular network neighbourhood and the vessel neighbourhood split into several classes, based on their diameters. We also focus on the vessels bifurcations, which are often missed by vesselness filters. We provide the code of the benchmark, which includes up-to-date C++ implementations of the seven filters, as well as the experimental setup (parameter optimization, result analysis, etc.). An online demonstrator is also provided to help the community apply and visually compare these vesselness filters. [ABSTRACT FROM AUTHOR]

In this article, the fast-scale instability in the three-level T-type single-phase inverter feeding diode-bridge rectifier with inductive load (3TSI-DR) is studied. Simulations suggest that such fast-scale instability on switching period scale can increase the harmonic content in the 3TSI-DR, which seriously affects its stable operation. To reveal the mechanism of this fast-scale instability, the state equation of the 3TSI-DR is derived, and state variables are solved based on quasi-static approximation principle. From state equation, the 3TSI-DR is periodic time-varying and piecewise smooth, belonging to Filippov system. Accordingly, the discrete-time mapping model of the 3TSI-DR is established, Filippov method is used for obtaining monodromy matrix, and Floquet theory is applied to explore instability mechanism. Theoretical results indicate that the fast-scale instability of the 3TSI-DR is caused by period-doubling bifurcation. Moreover, the Floquet multiplier sensitivities of different circuit parameters are calculated to identify key parameters; via comparing theoretical analyses with simulations, the unstable angle ranges of the fast-scale instability are given, and the stability boundaries in various parameter spaces are discussed. All these can provide design-oriented information for optimizing the 3TSI-DR to avoid instability due to period-doubling bifurcation. Finally, experimental results agreeing with simulations are presented to verify the correctness of theoretical analyses. [ABSTRACT FROM AUTHOR]

The loss of small signal stability under parameter variation (e.g., fluctuation of loads and wind powers) can be ascribed to local bifurcations, i.e., saddle-node, Hopf, singularity-induced, and limit-induced bifurcations. Classic bifurcation calculation methods like the direct method and continuation method can only provide a bifurcation point or two-parameter bifurcation curve. Based on Galerkin method and the implicit function theorem, this paper proposes accurate polynomial approximations of bifurcation hypersurfaces in the multi-dimensional parameter space of interest. The proposed method can ensure high accuracy in this parameter space, and thus is preferable to the existing Taylor expansion-based local approximation method, given the intrinsic large-variation characteristic of wind powers. Acquired bifurcation hypersurfaces are immediately used to construct the small signal stability region of the continuous system, and then compute the stability margin for the operating point subjected to uncertainty of wind generation. Besides, the validity scope of the proposed method is analyzed, and the handling of limit-triggered equation switching as well as its computational difficulty is discussed. Computational results on the two-parameter 11-bus two-area and six-parameter IEEE 145-bus test systems validate the high accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

A new smooth model is proposed in this paper to eliminate the non-differentiability of several types of limits in power flow models. The proposed smooth model accurately represents power system static models with limits as a continuously differentiable function. Analytic results are developed to show that each solution of the proposed smooth model is arbitrarily close to a solution of the corresponding original power flow model with limits. The proposed smooth model includes a wide range of devices with physical limits, such as generators, transformers, HVDCs, phase shifters, and shunts. In addition, it is shown that every generic static bifurcation in the original model is transformed into a saddle-node bifurcation in the smoothed model. Hence, the search for bifurcations in voltage stability assessment can be greatly simplified. Several numerical studies of the proposed smooth model on a 9241-bus power system and on a 13659-bus power system have shown promising results. [ABSTRACT FROM AUTHOR]

In this article, an inductive wireless power transmission (IWPT) system is a high-order nonlinear switching system with multiple operating modes. It is challenging to analyze the dynamic characteristics of such a system using the extended describing function, generalized state-space averaging, or other existing modeling methods. To address this challenge, this study proposes a modeling and dynamic characteristics analysis method for a closed-loop IWPT control system based on a sigmoid function model. A sigmoid function with a large steepness factor is adopted to approximate the switching process of the switch and a unified smooth continuous dynamic model is established for a phase-shift controlled IWPT system. Because this model is infinitely differentiable, a stability theory of continuous systems, such as the Floquet theory, can be directly applied to analyze the bifurcation type of the system and stability of periodic solutions. Analysis results reveal the transition of the phase-shift-controlled IWPT system from periodic behavior to chaotic behavior through saddle-node bifurcation and Neimark–Sacker bifurcation. A stable domain in the two-parameter space of the controller proportional coefficient and load is also obtained. Both simulation and experimental results validate the accuracy of the proposed model and theoretical analysis method, which can significantly reduce the difficulty of analyzing IWPT system dynamics. [ABSTRACT FROM AUTHOR]

Legged robots have excellent terrestrial mobility for traversing diverse environments and, thus, have the potential to be deployed in a wide variety of scenarios. However, they are susceptible to falling and leg malfunction during locomotion. Although the use of a large number of legs can overcome these problems, it makes the body long and leads to many legs being constrained to contact with the ground to support the long body, which impedes maneuverability. To improve the locomotion maneuverability of such robots, this study focuses on dynamic instability, which induces rapid and large movement changes, and uses a 12-legged robot with a flexible body axis. Our previous work found that the straight walk of the robot becomes unstable through a Hopf bifurcation when the body-axis flexibility is changed, which induces body undulations. Furthermore, we developed a simple controller based on the Hopf bifurcation and showed that the instability facilitates the turning of the robot. In this study, we newly found that the straight walk becomes unstable through a pitchfork bifurcation when the body-axis flexibility is changed in a way different from that in our previous work. In addition, the pitchfork bifurcation induces a transition into a curved walk, whose curvature can be controlled by the body-axis flexibility. We developed a simple controller based on the pitchfork bifurcation characteristics and demonstrated that the robot can perform a turning maneuver superior to that with the previous controller. This study provides a novel design principle for maneuverable locomotion of many-legged robots using intrinsic dynamic properties. [ABSTRACT FROM AUTHOR]

Percutaneous coronary intervention is widely applied for the treatment of coronary artery disease under the guidance of X-ray coronary angiography (XCA) image. However, the projective nature of XCA causes the loss of 3D structural information, which hinders the intervention. This issue can be addressed by the deformable 3D/2D coronary artery registration technique, which fuses the pre-operative computed tomography angiography volume with the intra-operative XCA image. In this study, we propose a deep learning-based neural network for this task. The registration is conducted in a segment-by-segment manner. For each vessel segment pair, the centerlines that preserve topological information are decomposed into an origin tensor and a spherical coordinate shape tensor as network input through independent branches. Features of different modalities are fused and processed for predicting angular deflections, which is a special type of deformation field implying motion and length preservation constraints for vessel segments. The proposed method achieves an average error of 1.13 mm on the clinical dataset, which shows the potential to be applied in clinical practice. [ABSTRACT FROM AUTHOR]

As chaotic systems are widely used in many fields, the study of them is becoming more and more in- depth. This paper first presents a new single-equilibrium chaotic system which is only three terms, and some fundamental dynamical feature of the new chaotic system are discussed, such as equilibria, dissipativity, Poincaré diagram, bifurcation graph, etc. Secondly, a new finite-time controllers is designed by using Lyapunov stability theory, and it can be used for bound synchronization of the general chaotic systems. In contrast to the current finite time controller of the chaotic system, the designed controller in this paper does not contain exponential term, it can be simple and eliminate the chattering phenomenon during synchronizationis, which may be easier to implement in practical application. In addition, under the finite time controller, the bound of control energy consumption of the chaotic system is estimated. Finally, the finite-time controllers for the new chaotic system are advanced using the design method of finite-time controller of the general chaotic system, and the result of numerical simulation is given to check its validity by the designed method.

Continuous-time memristor have been widely used in fields such as chaotic circuits and neuromorphic computing systems, however, research on the application of discrete memristors haven’t been noticed yet. In this paper, a new chaotic neuron is firstly designed by applying the discrete memristor to two-dimensional Rulkov neuron. And then the dynamical behaviors of the discrete memristor-based neuron are analyzed by experiments including phase diagram, bifurcation, and spectral entropy complexity algorithm. The results show that the resistance of memristor has an important effect on the system dynamics, which delays the occurrence of bifurcation, in particular, the bifurcation disappears and the system reaches the fixed point of the neuron when the resistance is greater than a threshold. It is also found that with the increase of the current gain, the bursting activity becomes higher in frequency and wider range of high complexity is obtained. The results of our study show that the performance of Rulkov neuron is improved by applying the discrete memristor, and may provide new insights into the mechanism of memory and cognition in the nervous.

Objective: The bifurcation of neuronal firing is one of important nonlinear phenomena in the nervous system and is characterized by a significant change in the rate or temporal pattern of neuronal firing on responding to a small disturbance from external inputs. Previous studies have reported firing bifurcations for individual neurons, not for a population of neurons. We hypothesized that the integrated firing of a neuronal population could also show a bifurcation behavior that should be important in certain situations such as deep brain stimulations. The hypothesis was verified by experiments of rat hippocampus in vivo. Methods: Stimulation sequences of paired-pulses with two different inter-pulse-intervals (IPIs) or with two different pulse intensities were applied on the alveus of hippocampal CA1 region in anaesthetized rats. The amplitude and area of antidromic population spike (APS) were used as indices to evaluate the differences in the responses of neuronal population to the different pulses in stimulations. Results: During sustained paired-pulse stimulations with a high mean pulse frequency such as ∼130 Hz, a small difference of only a few percent in the two IPIs or in the two intensities was able to generate a sequence of evoked APSs with a substantial bifurcation in their amplitudes and areas. Conclusion: Small differences in the excitatory inputs can cause nonlinearly enlarged differences in the induced firing of neuronal populations. Significance: The novel dynamics and bifurcation of neuronal responses to electrical stimulations provide important clues for developing new paradigms to extend neural stimulations to treat more diseases. [ABSTRACT FROM AUTHOR]

A large number of experiments have proved that the ring structure is a common phenomenon in neural networks. Nevertheless, a few works have been devoted to studying the neurodynamics of networks with only one ring. Little is known about the dynamics of neural networks with multiple rings. Consequently, the study of neural networks with multiring structure is of more practical significance. In this article, a class of high-dimensional neural networks with three rings and multiple delays is proposed. Such network has an asymmetric structure, which entails that each ring has a different number of neurons. Simultaneously, three rings share a common node. Selecting the time delay as the bifurcation parameter, the stability switches are ascertained and the sufficient condition of Hopf bifurcation is derived. It is further revealed that both the number of neurons in the ring and the total number of neurons have obvious influences on the stability and bifurcation of the neural network. Ultimately, some numerical simulations are given to illustrate our qualitative results and to underpin the discussion. [ABSTRACT FROM AUTHOR]

In this article, the slow-scale instability occurring in the three-level T-type inverter with a passive memristive (3LT2IPM) load is investigated. The average model of the 3LT2IPM, whose coefficient matrix is nonlinear periodic time-varying, is constructed, both harmonic balance method used to calculate the approximate solution of the average model and Floquet theory used to identify the circuit dynamic states are applied to explore the mechanism of the slow-scale instability emerging in the 3LT2IPM. Theoretical results indicate that the slow-scale instability of the 3LT2IPM is caused by Hopf bifurcation emerging in a region where the frequency is higher than line frequency but much lower than switching frequency. Also, the conditions of three theoretical parameters that make the theoretical analysis results as accurate as possible are presented. Different parameters impact on the stability boundary of the 3LT2IPM in various design parameter spaces are discussed, and the Floquet multiplier sensitivity is analyzed to identify key parameters for the stability of the 3LT2IPM, which are helpful to guide parameter adjustment of the 3LT2IPM to ensure its stable operation in practice. Finally, hardware experiment is established and experimental verification is provided. Physical experiments agree well with simulations, which together demonstrate the correctness of theoretical analysis. [ABSTRACT FROM AUTHOR]

An islanded microgrid consisting of grid-forming converters, being a high-order nonlinear system, exhibits rich nonlinear dynamical phenomena. The use of appropriate reduced-order models offers useful physical insights into the behavior of the system without the need for excessive computational resources. In this article, we derive a number of reduced-order models capable of describing the slow-scale dynamics of an islanded microgrid comprising a number of grid-forming converters. It is shown that slow-scale Hopf and homoclinic bifurcation behaviors arise from the stability of the voltage loops of grid-forming converters and are unrelated to the transmission network dynamics. Therefore, omitting the network dynamics does not affect the accuracy of reduced-order models in representing the slow-scale dynamics of the system. This is especially beneficial for modeling the microgrid with a complex transmission network. Furthermore, on this basis, all inner loops can be omitted when studying saddle-node bifurcation, leading to the development of power-flow-based reduced-order models. Finally, the stability of an islanded microgrid with a complex transmission network is evaluated. [ABSTRACT FROM AUTHOR]

Cascaded dc–dc converter is the main component of the dc distributed power system. It is valuable to establish the accurate model for studying the stability of cascaded dc–dc converters. However, the cascaded dc–dc system has many operating modes, such that the existing classic methods, e.g., state-space average model and discrete-mapping model, are difficult to explore to analyze cascaded dc–dc converter system, especially that with different switching frequencies. To overcome this drawback, this article promulgates a new modeling and stability analysis method for cascaded dc–dc converter. Small-step method, discretization method, and Euler method are exploited to modeling. All stages of the system are considered, therefore, accurate; and stability is divided into three categories according to the different definitions. Then, the cascaded systems with the same or different switching frequencies are studied using the presented method. As an example, two-stage peak current-mode controlled boost converter is scrutinized. Finally, simulations and experiments are manipulated to verify the correctness of the new method. [ABSTRACT FROM AUTHOR]

When used in engineering applications, most existing chaotic systems may have many disadvantages, including discontinuous chaotic parameter ranges, lack of robust chaos, and easy occurrence of chaos degradation. In this article, we propose a two-dimensional (2-D) parametric polynomial chaotic system (2D-PPCS) as a general system that can yield many 2-D chaotic maps with different exponent coefficient settings. The 2D-PPCS initializes two parametric polynomials and then applies modular chaotification to the polynomials. Setting different control parameters allows the 2D-PPCS to customize its Lyapunov exponents in order to obtain robust chaos and behaviors with desired complexity. Our theoretical analysis demonstrates the robust chaotic behavior of the 2D-PPCS. Two illustrative examples are provided and tested based on numeral experiments to verify the effectiveness of the 2D-PPCS. A chaos-based pseudorandom number generator is also developed to illustrate the applications of the 2D-PPCS. The experimental results demonstrate that these examples of the 2D-PPCS can achieve robust and desired chaos, have better performance, and generate higher randomness pseudorandom numbers than some representative 2-D chaotic maps. [ABSTRACT FROM AUTHOR]

Memristor can be designed based on the topological structure of a dynamical system. Lorenz system provides such a structure for memristor building, in which one of the system variables can be regarded as the internal variable of the mathematical model. Based on the strong load capacity of AD633, two such capacitors are coupled directly to construct a simplified chaotic circuit. The memristor parameter can rescale the amplitudes of the system variables directly. Although the memristive Lorenz system has similar properties of bifurcation and multistability to the original one, it shows more opportunities for memristor-based information processing. [ABSTRACT FROM AUTHOR]

The generation of self-sustaining oscillations at the output of nonlinear systems without tracking a reference signal is under investigation. In this study, we proposed an internal double fuzzy inference system to generate an asymptotically stable limit cycle or self-oscillations for the second-order systems. The fuzzy system has been synthesized by invoking the Poincaré–Bendixson theorem, which states sufficient and necessary conditions of existence of an attracting periodic orbit at the output of the closed-loop system. This theorem was also used for design; that is, we set the tuning rules of the fuzzy controller. The effectiveness of the proposed controller is corroborated by numerical simulations and experiments made in a single-link pendulum system. [ABSTRACT FROM AUTHOR]

With widespread application of voltage source converter (VSC) as a key energy-conversion power electronic device by using the phase-locked loop (PLL) technique for synchronization, the system dynamics has become much complicated. In this paper, the nonlinear dynamics and transient stability of the PLL-based VSC system are investigated, within a unified framework of the (normalized) generalized swing equation. It is found that there are three different types of bifurcation, including the generalized saddle-node, Hopf, and homoclinic bifurcations. Within the coexistence parameter region, the basin boundary of the stable equilibrium point shows either a closed-loop or a fish-like pattern. With the help of the equal area criterion (EAC), the transient stabilities under different transient disturbances including short circuit, voltage dip, and power rise are analyzed. Because the equivalent damping of the VSC is state-dependent, the theoretical results based on the EAC are examined. Furthermore, based on the analytical results from the generalized swing equation, the principle for all major transient stability enhancement methods is uncovered. All these findings are well verified by extensive electromagnetic transient simulations. Therefore, the generalized swing equation provides a deeper physical insight and plays a crucial role in transient stability problems in power-electronic-dominated power systems, similar to the swing equation in traditional power systems. [ABSTRACT FROM AUTHOR]

Bifurcation analysis and dynamical system studies are carried out to find the stability regime and chaotic scenario in electron acoustic waves in relativistic degenerate plasma. We have obtained the quantum hydrodynamic model and obtain the Korteweg–de Vries equation describing the nature and characteristics of solitary structures. The amplitude modulated envelop soliton formation due to external perturbations has been studied by analyzing the nonlinear Schrodinger equation. Further to study the stability factors and the parametric range for such stability, the dynamical system is studied and bifurcation analysis has been carried out. The chaotic behavior of the system is studied through largest Lyapunov exponent (LLE). This work will find application in theoretically predicting the stable modes in many solar plasma and stellar plasma applications and in laser plasma in future. [ABSTRACT FROM AUTHOR]

Dynamic and nonlinear systems are emerging as potential candidates for random bit generation. In this context, chaotic systems, which are both dynamic and stochastic, are particularly suitable. This article introduces a new continuous chaotic system along with its corresponding implementation, which targets FPGA (fpga). This chaotic system has five dimensions, which exhibit complex chaotic dynamics, thus enabling the utilization of chaotic signals in cryptography. A mathematical analysis is presented to demonstrate the dynamic characteristics of the proposed hyperchaotic system. A novel digital implementation of the proposed system is presented. Moreover, a data scrambling circuit is implemented to eliminate the bias effect and increase the randomness of the bitstream generated from the chaotic signals. We show that the proposed random bit generator has high randomness. The generated bits successfully pass well-known statistical randomness test-suites, i.e., NIST SP800-22, Diehard, and TestU01. The ready-to-use random bit generator is deployed on a Xilinx Zynq-7000 SoC ZC702 Evaluation Kit. Experimental results show that the proposed random bit generator can achieve a maximum throughput of 6.78 Gb/s, which is over 3.6 times greater than state-of-the-art designs, while requiring under 4% of the resources available on the targeted FPGA. [ABSTRACT FROM AUTHOR]

The aim of this article is to analyze the parameter stability and power transfer limits of active distribution networks with power converters and load tap changers by using bifurcation theory.First, the nonlinear model of a representative distribution grid with mixed loads and power converters is derived. Frequently neglected effects of converter capacity limits and transformers with load tap changers are considered, and for this purpose, static and dynamic saturations are modeled by using approximations based on smooth functions. In addition, a solution based on an antiwindup scheme is provided to model load tap changers without numerical convergence problems. These methods allow their integration to the model in a comprehensive way. Results show the impact of converter parameters and its limits on system stability as well as the impact of weak grid conditions. Moreover, they show that these effects can destabilize the system under, seemingly, safe operating conditions. The results indicate that reactive power support from converters can improve stability margins and the performed analysis can help in the design of the converter control parameters. Experimental results obtained from the laboratory environment comprising two distributed generators and a grid emulator are used for the validation of the contributions of this article. [ABSTRACT FROM AUTHOR]

When a peak-current-mode controlled (PCMC) boost converter operates at $D>0.5$ , instabilities such as bifurcations and chaos severely restrict its operation range. This brief proposed a logarithm-type slope compensation (LTSC) to use small amplitude signal to provide enough compensations. Firstly, with the aim of minimizing the error magnification of the input current, the proposed LTSC is deduced. Secondly, the comparisons between the proposed LTSC and other slope compensation (SC) methods are made. Finally, simulations and experiments are carried out to verify the theoretical analysis. The research offered a novel SC to suppress instabilities in PCMC boost converter when $D>0.5$. The proposed LTSC has advantages such as: (1) LTSC uses smaller amplitude to stabilize the converter; (2) LTSC extend the stable region of boost converter; (3) LTSC can be applied in other PCMC dc-dc converters. [ABSTRACT FROM AUTHOR]

This work investigates an injection-locked power oscillator inductively coupled to an external resonator for wireless power transfer. The system allows a high transfer efficiency, while ensuring a constant oscillation frequency versus the coupling factor, unlike free-running implementations. An analytical formulation provides insight into the impact of the coupling factor on the locked-operation ranges. Two types of qualitative behavior, delimited by a codimension-two bifurcation, are distinguished. The investigation is extended to a Class-E oscillator at 13.56 MHz, analyzed with a new harmonic balance (HB) method that provides the family of locked-solution curves in a single simulation. Very good agreement is obtained with the measurement results. [ABSTRACT FROM AUTHOR]

In this paper, a model of miR-9/Hes1 interaction network involving one time delay and diffusion effect under the Neumann boundary conditions is studied. First of all, the stability of the positive equilibrium and the existence of local Hopf bifurcation and Turing-Hopf bifurcation are investigated by analyzing the associated characteristic equation. Second, a algorithm for determining the direction, stability and period of the corresponding bifurcating periodic solutions is presented. The obtained results suggest that the quiescent progenitors (high steady-state Hes1) can be easily excited into oscillation by time delay whereas the differentiated state (low steady-state Hes1) is basically unaffected, and the integrated effect of delay and diffusion can induce the occurrence of spatially inhomogeneous patterns. More importantly, spatially homogeneous/inhomogeneous periodic solutions can exist simultaneously when the diffusion coefficients of Hes1 mRNA and Hes1 protein are appropriately small, conversely, there is only spatially homogeneous periodic solutions. Intriguingly, both temporal patterns and spatial-temporal patterns show that time delay can prompt Hes1 protein to shift from the high concentration state to the low concentration one (“ON” $\rightarrow$ → “OFF”), where Hes1 protein shows low level whereas miR-9 shows high level. Finally, some numerical examples are presented to verify and visualize theoretical results. [ABSTRACT FROM AUTHOR]

This work presents an investigation of the nonlinear dynamics of an oscillator that is inductively coupled to an external resonator for power transfer applications. Analytical expressions are derived for the oscillation frequency and output power, which provide insight into the effect of the coupled resonator on the oscillator solution. From the analytical study, criteria are derived to maximize the $k$ range with a high efficiency and a limited variation of the oscillation frequency. The resistor of the external resonator can be modulated for data transmission to the core oscillator. Here the sensitivity to this resistor and its dependence on the coupling factor are analyzed in detail. The methods have been applied to a Class-E oscillator that has been analyzed through a contour-intersection technique. This is based on the extraction from harmonic balance (HB) of a bi-variate nonlinear admittance function accounting for the oscillator circuit, which is combined with the passive linear admittance function of the coupled resonator. The advantage is taken of the ease of this analysis to obtain constant-efficiency contours in the oscillatory regime, traced in the plane defined by the coupling factor and any suitable analysis parameter. By means of a bifurcation analysis, various phenomena, including the oscillation extinction plus onset versus the coupling factor and the appearance of quasi-periodic solutions, are detected and avoided. Very good correspondence has been obtained between simulation and measured results. [ABSTRACT FROM AUTHOR]

This article presents a detailed study on the basic features of bifurcation of dust ion acoustic (DIA) traveling waves in a dusty plasma comprising warm adiabatic ions, nonextensive electrons, and arbitrarily charged dust particles. A reduced dynamical system is obtained for plasma waves’ evolution, and the global dynamics of local bifurcation of waves’ motion are determined on the equilibrium points’ dust concentrations’ plane with respect to all possible plasma parametric combinations. The stability and phase portrait analysis indicate a sudden emergence of nonlinear periodic and solitary waves for critical values of negative (positive) dust concentration. At these critical values, waves’ dynamics exhibit a transcritical bifurcation with half-stable fixed points which support new spike-like traveling waves. The analytical and numerical solutions reveal that the decay rate of this localized structure is much slower than ordinary solitary waves that decay exponentially fast. Furthermore, the existence domain of bifurcation parameters and transitions between modes are found for different values of nonextensive electrons and arbitrarily charged dust concentrations. Our results could be applicable to different space and astrophysical plasma systems, particularly in earth atmosphere. [ABSTRACT FROM AUTHOR]

In the modern world of technology, the cascaded DC-DC converters with multiple output configurations are contributing a dominant part in the DC distribution systems and DC micro-grids. An individual DC-DC converter of any configuration exhibits complex non-linear dynamic behavior resulting in instability. This paper presents a cascaded system with one source boost converter and three load converters including buck, Cuk, and Single-Ended Primary Inductance Converter (SEPIC) that are analyzed for the complex non-linear bifurcation phenomena. An outer voltage feedback loop along with an inner current feedback loop control strategy is used for all the sub-converters in the cascaded system. To explain the complex non-linear dynamic behavior, a discrete mapping model is developed for the proposed cascaded system and the Jacobian matrix’s eigenvalues are evaluated. For the simplification of the analysis, every load converter is regarded as a fixed power load (FPL) under reasonable assumptions such as fixed frequency and input voltage. The eigenvalues of period-1 and period-2 reveal that the source boost converter undergoes period-2 orbit and chaos whereas all the load converters operate in a stable period-1 orbit. The proposed configuration eliminates the period-2 and chaotic behavior from all the load converters and is also validated using simulation in MATLAB/Simulink and experimental results.

Harmonic balance provides steady-state solutions only and has significant shortcomings when addressing oscillatory regimes. As a result, complementary methodologies are required both to ensure the stability of the solution obtained and to design/simulate oscillator circuits. The complexity of the stability analysis increases with the number of active elements and the intricacy of the topology, so there can be uncertainties in the case of complex structures. On the other hand, as recently demonstrated oscillators enable a compact and low-cost implementation of RFID readers and radar systems, which comes at the expense of a more complex performance, very difficult/impossible to simulate with commercial HB. This work presents a review of recent advances on stability and oscillation analysis at circuit level and through semi-analytical formulations. At circuit level, a method for the stability analysis of complex microwave systems is presented, based on the calculation of the characteristic determinant, extracted from the commercial simulator through a judicious partition of the system into simpler blocks. This determinant will be used for the first time to obtain the stability boundaries through a contour-intersection method, able to provide multivalued and disconnected curves. At a semi-analytical level, a realistic numerical model of the standalone oscillator, extracted from HB simulations, is introduced in an analytical formulation that describes the oscillator interaction with other elements. Here it will be applied to a self-injection locked radar, in which the oscillator is injected by its own signal after this signal undergoes propagation and reflection effects. A procedure to determine the stability properties considering the time delay of the signal envelope is presented for the first time. Using the same self-injection concept, a new stabilization method to reduce the phase-noise of an existing oscillator with minimum impact on its original frequency is described.

The dynamics of neural networks has been widely concerned by scholars. However, most of the previous results on dynamical bifurcations are limited to few nodes coupling neural networks which modeled by differential equations with integer-order derivative, and few efforts have been contributed to studying the bifurcation behaviors of large-scale fractional-order neural networks. Furthermore, the structural characteristics of networks are also of great research value. Among them, the ring structure is a common phenomenon in neural networks. Although there are few papers on the bifurcation analysis of ring-structured neural networks recently, they consider only the case of a single ring. In this article, the dynamical analysis and design for a class of large-scale-delayed fractional-order neural networks with multiple rings and hub structure are investigated. First, the time delay is considered to be the bifurcation parameter and the formula of Coates’ flow graph is adopted to obtain the characteristic equation of large-scale networks. Second, by analyzing the complex radial and circular connections of neurons, the delay-induced Hopf bifurcation sufficient conditions for the neural network are established. Finally, the theoretical results are substantiated by a number of numerical simulation experiments and the relationships between the onset of bifurcation and the fractional order, the number of neurons, and the number of rings are revealed. [ABSTRACT FROM AUTHOR]

Adaptive synaptic neuron model involves complex activation functions. These nonlinearities lead to complicated hardware implementations, which greatly hinder neuron-based applications. To effectively solve this issue, a piecewise-linear (PWL) activation function with simplified circuit implementation is presented for the adaptive synaptic neuron model in this brief. With this neuron model, the stability evolution mechanism of the equilibrium state is analyzed and the parameter- and initial condition-related neuron dynamics are numerically explored. Afterwards, an analog circuit is designed and manually made using commercially available components. The phase trajectories captured by the hardware experiments verify the feasibility of the PWL activation function. Thus, such a PWL simplification shows superiority in emulating neuron dynamics. [ABSTRACT FROM AUTHOR]

Compared with continuous memristor, discrete memristor has not been deeply studied. In this work, a new discrete memristor model and its pinched hysteresis loops are explored. Based on this model, a simple 2D hyperchaotic map and its dynamics are exhibited. Reservoir computing is an extension of neural networks, which has been received adequate attention. So far, the application of discrete memristor on reservoir has not been reported. To this end, we consider the discrete memristor-based map as a reservoir and verify its performance by a nonlinear regression task. The results indicate that the memristor-based map can be used effectively as a reservoir and enable reservoir computing systems go further on the way of efficient processing temporal signals in the future. [ABSTRACT FROM AUTHOR]

Bifurcation amplifiers are two-state systems that behave as flip-flops. We propose a two-bit shift register with coupled bidirectional bifurcation amplifiers. We consider a model of the amplifier that is based on a driven nonlinear vibrational system with Duffing nonlinearity. A discussed physical implementation is a nano-mechanical system. The analysis of bifurcation points provides a design framework for driving forces. We use a modulated two-level pulse at the first amplifier and a periodic three-level pulse at the second. We numerically demonstrate that these driving forces allow for the transfer of digital data between each amplifier. Our investigation provides an alternative approach for developing digital shift registers using nonlinear dynamics at the nanoscale. [ABSTRACT FROM AUTHOR]

Cordless kitchen appliances powered by wireless power transfer (WPT) technology can operate without the clutter of cords, making them safer and easier to clean. In order to allow cordless kitchen appliances to be placed more freely, this article proposed a parity-time (PT) symmetric WPT system with stable output power in the whole coupling range. Here, a new implementation of a PT-symmetric circuit using a combination of self-oscillating methods and pulsewidth modulation (SO-PWM) is presented. The self-oscillating mode is activated in the strong coupling region, which guarantees a constant output power and constant transfer efficiency against the coupling coefficient variation. In the weak coupling region, the PWM mode with a fixed frequency and a variable duty cycle is adopted, and a control strategy based on primary-side-only parameters is presented to obtain stable power transmission. Besides, a corresponding coupling-region detection method based on the reflected resistance is proposed to ensure smooth switching between SO mode and PWM mode. The advantage is that the stable output power can be maintained in the whole coupling region without any extra dc–dc converter and dual-side communication requirements, while maintaining the same transfer efficiency as the standard PT-symmetric WPT system. A 500-W experimental prototype is built to verify the theoretical analysis. The results show that with a transfer efficiency of over 91.6%, the misalignment tolerance can be increased by 172%. [ABSTRACT FROM AUTHOR]

It is well-known that the ripple control technique benefits from fast load transient response and small cross regulation for single-inductor dual-output (SIDO) dc–dc converter. However, existing capacitor current ripple (CCR) controlled SIDO buck converter suffers from incomplete operation state and single switching path. Thus, it has a limited stable load range. In order to extend the stable load range and suppress cross regulation of SIDO buck converter in continuous conduction mode (CCM), a novel ripple control technique, called as capacitor current and capacitor voltage ripple (CCVR) control, is proposed in this article. The operation principle of the proposed CCVR controlled SIDO CCM buck converter is presented, and its discrete iterative map model is established. Furthermore, the stability and stable load range have been discussed by using bifurcation diagrams. Based on the established small signal model, Bode plots are given to show the performance in suppressing cross regulation. Finally, simulation and experiment results are provided to verify the theoretical analysis. It shows that the proposed CCVR control technique can be applied to SIDO CCM buck converter to extend its stable load range and suppress its cross regulation. [ABSTRACT FROM AUTHOR]

Bifurcation-based sensors, implementing stability boundaries monitoring in bistable microstructures, may manifest higher sensitivity and robustness when compared to their statically operated counterparts. In the operation of these devices, two key questions arise: 1) how to reliably identify the critical events associated with the transition between two stable states; 2) what is the maximal sampling rate allowing to identify these critical events in a periodically actuated device. Motivated by the potential implementation as a bifurcation-based flow sensor, in this work we experimentally explore the transient snap-through (ST) and snap-back (SB) dynamics of a bistable initially curved ($500 \,\mu \text{m}$ long and $2.5\, \mu \text{m}$ wide) electrostatically actuated single-crystal Si microbeam. We employ a threshold-based approach for the ST and SB events detection and identify two mechanisms determining the maximal sampling frequency of the device: a phase lag between the voltage signal and the mechanical response and free decaying vibrations following the buckling event. In accordance with our experimental results and consistently with the reduced-order model predictions for the bistable beam operating at atmospheric pressure, at the actuation signal frequency of $\approx 0.6$ KHz, which is still much lower than the beam’s natural frequency of $\approx 110 $ KHz, the free oscillations engendered by one critical event (ST or SB) interfere with the consecutive one, preceding its emergence. On the other hand, an inherent phase lag ultimately hinders the abrupt ST and SB transitions at these actuating frequencies. [2021-0091] [ABSTRACT FROM AUTHOR]

Spin-polarized vertical-cavity surface-emitting lasers (spin-VCSELs) are known to support high-frequency continuous birefringence-induced oscillations whose frequency is not determined by the relaxation oscillation (RO) mechanism usually recognized in conventional laser diodes. However, this depends on the pumping condition as well as some key parameters. For example, the reported hybrid pumping consisting of standard electrical pumping and polarized light pulse excitation only results in damped high-frequency birefringence-induced oscillations. Here we focus on the optically pumped spin-VCSELs which have not been fully understood compared to those under hybrid pumping. We consider both periodic and continuous-wave (CW) regimes for exploiting high-frequency operation. In the periodic regime, the regions of period-one (P1) oscillations are identified via bifurcation diagrams and peak amplitude curves/maps, where the dependence on some key parameters is systematically studied. In the CW regime, we explore the high-frequency polarization modulation. In particular, double peak response curves are found when spin-VCSELs are pumped with a certain polarization degree and the RO frequency related peak in the frequency response curve is extremely sensitive to the variation of the polarization degree, which leads to rich modulation dynamics in spin-VCSELs. Additionally, the effects of the spin relaxation rate on the polarization modulation bandwidth are illustrated by using two-parameter bandwidth maps. These findings help us better understand the underlying high-frequency dynamics of the optically pumped spin-VCSELs. [ABSTRACT FROM AUTHOR]

This article discusses a rigorous and straightforward method to synthesize and design a transmission-line-based reflectionless bandstop filter with high performance in terms of reflectionless range. Our design strategy targets to allow a reflectionless bandstop filter to feature three distinguished advantages that are incomparable to others. First, the presented filter structure is capable of producing an exceptional broadband impedance matching performance. Second, it can be designed to have an extended upper passband. Third, an ${N}$ th-order filter has ${N}$ coupling structures and each of them is used twice in design. Hence, it is required to design and tune only ${N}$ coupling structures, whereas other design approaches use more than ${N}$ distinct coupling structures. Although reflectionless filters having one of the aforementioned features have been reported, one exhibiting all the characteristics has never been reported to date. Fabricated filter examples fully validate the design theory. [ABSTRACT FROM AUTHOR]

Polynomial functions have been the main barrier restricting the circuit realization and engineering application of multiwing chaotic systems (MWCSs). To eliminate this bottleneck, we construct a simple MWCS without polynomial functions by introducing a sinusoidal function in a Sprott C system. Theoretical analysis and numerical simulations show that the MWCS can not only generate multibutterfly attractors with an arbitrary number of butterflies, but also adjust the number of the butterflies by multiple ways including self-oscillating time, control parameters, and initial states. To further explore the advantage of the proposed MWCS, we realize its analog circuit using commercially available electronic elements. The results demonstrate that in comparison to traditional MWCSs, our circuit implementation greatly reduces the consumption of electronic components. This makes the MWCS more suitable for many chaos-based engineering applications. Furthermore, we propose an application of the MWCS to chaotic image encryption. Histogram, correlation, information entropy, and key sensitivity show that the simple image encryption scheme has a high security and reliable encryption performance. Finally, we develop a field-programmable gate array test platform to implement the MWCS-based image cryptosystem. Both theoretical analysis and experimental results verify the feasibility and availability of the proposed MWCS. [ABSTRACT FROM AUTHOR]

This paper proposes an inequality constraints based method to efficiently and quickly estimate stability regions of droop control slopes for modular multilevel converter (MMC)-based multi-terminal dc (MTDC) systems. At first, a general small-signal model of the MMC-MTDC system is developed, which consists of the dc network and the MMCs with $dq$ controllers and multiple droop controllers. When deriving corresponding nonlinear state-space models, the edge-node matrix is introduced for the dc network modeling with arbitrary grid topology and transmission line model. Then, based on the eigenvalues sensitivity and the Taylor Series of eigenvalues, a set of inequality constraints are proposed to expeditiously estimate the suprema of the droop slopes and identify the droop slope stability regions for the MMC-MTDC system. To verify the state-space model, a comparison of dynamic responses between the math model calculation in MATLAB and the EMT simulation in PSCAD/EMTDC is conducted, which demonstrates the accuracy and the correctness of the developed small-signal model. The effectiveness of the proposed parameter stability region estimation method is demonstrated by several examinations including the supremum tests of droop slopes, the stability region sketches on accuracy, and the predicted unstable operations in PSCAD/EMTDC. [ABSTRACT FROM AUTHOR]

Fractal and chaos are two major phenomena in nonlinear systems. A few combinations of chaos with fractal for generating multiscroll attractors are reported. Thus, based on Chua multiscroll chaotic systems, a novel multiring chaotic system is proposed via Julia multifractal processes. The main purpose of this work is to make up for the deficiency of various fractal processes to further improve the performance of chaotic systems. A new class of multiscroll attractors is generated by combining different fractal processes, including symmetrical multiring attractor, separated multiring attractor, and nested multiring attractor. Furthermore, dynamic behaviors of the fractal chaotic system are analyzed by means of Lyapunov exponents and bifurcation diagram to indicate that the system exhibits chaotic characteristics. Experiments on the spectrum entropy (SE) complexity and image encryption performance demonstrate the good performance of the proposed fractal-based attractors. To verify the feasibility of multiring chaotic system, the various fractal-based attractors generated are implemented by micro controller unit (MCU), and the separated multiring attractors are observed on the digital oscilloscope. [ABSTRACT FROM AUTHOR]

Phase balancing of American-type three-phase distribution circuits is one of the classical problems faced by distribution system operators and planners. In this paper, a mixed-integer non-linear programming problem is formulated to minimize the number of phase connection changes in existing circuits to reach the desired phase balancing. The proposed algorithm uses geographical information system models of distribution circuits to build a reduced model and realistic load profiles offered by smart meters, or measurements at the distribution transformers to characterize the demand. The formulation is validated in highly unbalanced distribution circuits with thousands of single-phase customers. The results show that it is possible to rebalance large-scale circuits by moving a few single-phase laterals and loads. In addition, the application of the proposed method, based on loading conditions at different hours of the day, pointed out the same places to make the changes. [ABSTRACT FROM AUTHOR]

Under transient disturbance, the grid-forming voltage-source converter may lose its synchronization with the grid, inducing sustained low-frequency oscillation in instantaneous power, current, and phase angle. The physical origin of such oscillations is found to be a homoclinic bifurcation in this article. Before the system runs into a homoclinic bifurcation, a stable equilibrium point (SEP) and a stable periodic orbit coexist. When a large transient disturbance is applied, the system exhibits a periodic orbit, which manifests itself as low-frequency oscillation. Moreover, after the homoclinic bifurcation, the periodic orbit subsides, and only a single attractor, the SEP, exists in the phase space. In this case, the grid-forming converter is able to resynchronize with the grid even under transient disturbances. Bifurcation diagrams are derived as the boundaries of stable operation in the parameter space, which serve as practical design guidelines to avoid sustained oscillations. Cycle-by-cycle simulations and laboratory experiments are performed to verify the analytical findings. [ABSTRACT FROM AUTHOR]