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Motivated by the study of multiple time scale system dynamics, we analyze the Murali–Lakshmanan–Chua (MLC) dissipative circuit exhibiting periodic bursting with different types of oscillations in this paper. Such patterns can be analyzed by treating the slow variable as a parameter of the nonsmooth fast subsystem. The discontinuous bifurcation structure of the subsystem can be described by the generalized differential of Clarke and the Jacobian matrix of the system. Bursting patterns as well as the oscillation mechanisms can be clarified by the discontinuous bifurcations, time series and phase portraits. For the chosen circuit parameter values, this designed circuit admits both MLC type bursting attractors and Duffing–van der Pol circuit type bursting attractors. It is found that not only the features combined with the circuit parameters of the system, but also the two switching boundaries may have an important impact on the origin of the bursting behaviors. In particular, the explicit analytic solutions of the proposed circuit are investigated in detail. We also show that the bursting can arise from either discontinuous saddle-node bifurcation or slow passage through a discontinuous Hopf bifurcation. Finally, the validity of the theoretical analysis has been well verified by the numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, a new chaotic memristor system is developed based on a well-known nonlinear circuit. By replacing the nonlinear positive conductance of Shinriki's circuit with a memristor emulator, the new simple chaotic circuit can reduce the number of active elements and reduce power consumption. An analysis of equilibria and stability, dissipative properties, Lyapunov exponents, Kaplan-Yorke dimensions, and bifurcation diagrams is presented as well as numerical simulation of the new memristor chaotic system. As a final step, the electronic circuit is designed using Multisim software, which is complemented by a physical realization to demonstrate the feasibility of the chaotic system. • A new chaotic memristor system based on a well-known nonlinear circuit is proposed. • The new memristor has the advantage of reducing the number of active elements and reducing power consumption accordingly. • The proposed chaotic system is studied by analyzing its equilibrium and stability, dissipative properties, Lyapunov exponents, Kaplan-Yorke dimension, and bifurcations diagrams. • Multisim software is used to design the electronic circuit, while a physical realization is provided to demonstrate the system's feasibility. [ABSTRACT FROM AUTHOR]

Anisotropic impedance surfaces have been used to control surface wave propagation, which has benefited applications across a variety of fields including radio-frequency (RF) and optical devices, sensing, electromagnetic compatibility, wireless power transfer, and communications. However, the responses of these surfaces are fixed once they are fabricated. Although tunable impedance surfaces have been introduced by utilizing power-dependent nonlinear components, such a tuning mechanism is generally limited to specific applications. Here we propose an additional mechanism to achieve tunable anisotropic impedance surfaces by embedding transient circuits that are controllable via the type of incident waveform. By switching between the open and short states of the circuits, it is possible to separately control the unit-cell impedances in two orthogonal directions, thereby changing from an isotropic impedance surface to an anisotropic impedance surface. Our simulation results show that a short pulse strongly propagates for both x and y directions at 3 GHz. However, when the waveform changes to a continuous wave, the transmittance for x direction is reduced to 26%, although still the transmittance for y direction achieves 77%. Therefore, the proposed metasurfaces are capable of guiding a surface wave in a specific direction based on the incident waveform even with the same power level and at the same frequency. Our study paves new avenues regarding the use of surface wave control in applications ranging from wireless communications to sensing and cloaking devices.

This work advances the application of neural ordinary differential equations (ODEs) to circuit modeling. Prior works primarily utilized the recurrent neural network (RNN), which is a specific type of neural ODE. In this work, the capability of neural ODEs to represent different types of circuits is studied. Stability conditions are presented, both for neural ODEs in a standalone configuration and for neural ODEs with feedback connections, and practical techniques to impose the stability constraints during training are demonstrated. Based on the theoretical and experimental results, this work provides guidance as to when and how an accurate and stable neural ODE circuit model can be generated. [ABSTRACT FROM AUTHOR]

A model of a nonlinear beam with a piezoelectric patch linked to a nonlinear circuit is considered. The physical and mechanical parameters of the system are such that it presents a 1:3 internal resonance. The aim is to study, for different time scales, the effect of the nonlinearity of the electrical circuit on energy exchanges between the resonant modes. In fact, we would like to master energy channelling between two internally resonant modes of a composite beam via a nonlinear circuit. The investigations are carried out on the projected system equations on its internally resonant modes. The system behaviours at different scales of time are studied by coupled methods of complexification and multiple scale. Analytical developments permit to reveal different system dynamics characterized by periodic and/or non-periodic regimes. Finally, the paper is accompanied by comparisons between systems equipped with a resonant circuit (linear) and a nonlinear one. [ABSTRACT FROM AUTHOR]

The IEEE 1459 standard states that: “There is a need to quantify correctly the distortions caused by the nonlinear and parametric loads …” The paper undertakes this problem. The article includes an analysis of selected steady-state properties of a single-phase AC circuit containing a series connection of a resistance, an inductance, and a nonlinear element described by a signum function. The circuit is supplied from a sinusoidal voltage source. The mathematical model of this circuit is described using dimensionless variables. Based on the harmonic balance, a description of the circuit for the fundamental harmonic and the circuit for the remaining harmonics was separated. On the basis of the relationship between the current and voltage waveforms, the solution for all harmonics, the harmonic content coefficients, and the elements of the equivalent scheme of the nonlinear load, were estimated symbolically. Based on the circuit equations, a circuit model and measurement systems were developed in Simulink, as well as a program that controls these models in MATLAB and determines the characteristics of the circuit model. The paper presents selected circuit characteristics as a function of load voltage amplitude and circuit resistance. The conclusions drawn from these studies have practical significance.

Phase-locked loops (PLLs) are now widely used in communication systems and have been a classic system for more than 60 years. Well-known mathematical models of such systems are constructed in a number of approximations, so questions about how they describe the experimental dynamics qualitatively and quantitatively, and how the accuracy of the model description depends on the dynamic mode, remain open. One of the most direct approaches to the verification of any model is its reconstruction from the time series obtained in experiment. If it is possible to fit the model to experimental data and the resulting parameter values are close to the expected values (calculated from the first principles), the quantitative correspondence is nearly proved. In this brief, for the first time, the equations of the PLL model with a bandpass filter are reconstructed from experimental signals of the generator in various modes. The reconstruction shows that the model known from literature generally describes the experimental dynamics in regular and chaotic regimes. The relative error of parameter estimation is between 2% and 50%. The reconstructed nonlinear function of phase is not harmonic and highly asymmetric in contrast to model one. [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 designs a simple mathematical model for the voltage-controlled locally-active memristor (LAM), which undoubtedly simplifies the theoretical analysis. Owing to the N-shaped outline of the DC V -I curve, this LAM is called as N-shaped LAM. The small-signal analysis method is exploited to obtain the equivalent circuit of the N-shaped LAM when it is biased into the locally-active region. The calculation results show that the LAM can be equivalent to a conductance with a parasitic capacitor, which makes for a deep insight into the mechanisms at the origin of LAM based oscillator. The theoretical analysis reveals that the N-shaped LAM along with an inductor and a battery can generate oscillation, which is confirmed by the numerical simulation. In addition, observe from simulation results that as the inductance increases, the oscillation behavior of the system deviates from the sinusoidal signal and tends to a relaxation oscillation. Finally, the physical circuit realization of the N-shaped LAM based oscillator including the memristor emulator is proposed. The good agreement between the experimental results and simulation results further demonstrates the correctness and feasibility of the theoretical design and analysis.

For the first time, the physical memristor-based circuits i.e., HP TiO2 memristor-based circuits, of both series and parallel structures, have been extensively analyzed in the fractional domain by means of the state of the art yet simple fractional conformable derivative-based differential equations. Different outcome from the hypotheticalmemory element-based previous researches have been obtained. The dimensional consistencies of the fractional derivatives have also been concerned. The often-cited Joglekar’s window function has been adopted for modelling the boundary effect of the memristor and adding more nonlinearity close to the bounds of the memristor’s state variable. The formulated fractional differential equations have been solved and the related electrical quantities have been determined. The computational simulations have been performed. The stability analyses of both circuits have also been presented where it has been mathematically verified that only these HP TiO2 memristor-based circuits are stable always due to the boundary effect which does not exist in hypothetical elements assumed in those previous works. We also point out that that only those HP TiO2 memristor-based circuits of order higher than 3 are capable to exhibit the complex dynamics as such memristor lacks the local activity.

This article deals with the behavior and design of a homogeneous beam linked to an electrical absorber, via a piezoelectric material patched on the beam. The beam presents a cubic nonlinearity, which is consistent with geometrical nonlinearities for clamped-free beams. A cubic nonlinearity is added to the electrical circuit for similarity purposes. The coupled electromechanical equations are reduced to a two degrees of freedom system. The equation representing the mechanical response of the system is seen as the main system, whereas the equation coming from the electrical circuit would represent a nonlinear absorber. An analytical treatment at different time scales is endowed to identify electrical coefficients allowing the design of the electromechanical vibration absorber behavior. The equilibrium and singular points are identified, allowing the definition of ranges of forcing amplitudes leading to periodic and modulated regimes. The analytical results are compared with those obtained from direct numerical integration of the two degree of freedom system. [ABSTRACT FROM AUTHOR]

For the first time, the physical memristor-based circuits i.e., HP TiO2 memristor-based circuits, of both series and parallel structures, have been extensively analyzed in the fractional domain by means of the state of the art yet simple fractional conformable derivative-based differential equations. Different outcome from the hypotheticalmemory element-based previous researches have been obtained. The dimensional consistencies of the fractional derivatives have also been concerned. The often-cited Joglekar's window function has been adopted for modelling the boundary effect of the memristor and adding more nonlinearity close to the bounds of the memristor's state variable. The formulated fractional differential equations have been solved and the related electrical quantities have been determined. The computational simulations have been performed. The stability analyses of both circuits have also been presented where it has been mathematically verified that only these HP TiO2 memristor-based circuits are stable always due to the boundary effect which does not exist in hypothetical elements assumed in those previous works. We also point out that that only those HP TiO2 memristor-based circuits of order higher than 3 are capable to exhibit the complex dynamics as such memristor lacks the local activity. [ABSTRACT FROM AUTHOR]

This brief proposes a simple autonomous chaotic circuit based on minimum discrete component implementation. First, the circuit employs only five discrete components, including one op-amp, one resistor, one inductor, and two capacitors. Second, the circuit equations have six linear terms and one invariant dead-zone nonlinearity. Third, the circuit is robust stand-alone and has the most common implementation. The comprehensive dynamical behaviors are analyzed by using two-parameter bifurcation diagrams, Lyapunov exponents, and phase plots. The experimental demonstrations validated the analyses. [ABSTRACT FROM AUTHOR]

In this paper, a new class of systems with nonclassical jump resonance behavior is presented. Although jump resonance has been widely studied in the literature, this contribution refers to systems presenting a multiple hysteresis jump resonance phenomenon, meaning that the frequency response of the system presents more hysteresis windows nested within the same range of frequency. The analytical conditions for observing this type of behavior are derived and a design strategy to obtain multiple hysteresis jump resonance in circuits and systems presented. [ABSTRACT FROM AUTHOR]

In the last decade, researchers, who work in the field of nonlinear circuits, have the "dream" to use a real memristor, which is the only nonlinear fundamental circuit element, in a new or other reported nonlinear circuit in literature, in order to experimentally investigate chaos. With this intention, for the first time, a well-known nonlinear circuit, in which its nonlinear element has been replaced with a commercially available memristor (KNOWM memristor), is presented in this work. Interesting phenomena concerning chaos theory, such as period-doubling route to chaos, coexisting attractors, one-scroll and double-scroll chaotic attractors are experimentally observed. [ABSTRACT FROM AUTHOR]

The parameters of a harmonic source change with the fluctuating background voltage and current in electric power system, which makes it difficult to establish accurate harmonic models. To solve this problem, a dynamic parameter model (DPM) for harmonic source networks is proposed in this paper. By equating the parameters of a harmonic source as a polynomial of voltage and current, the proposed model can adjust parameters accordingly. The model is not only suitable for a single harmonic source but also for complex harmonic source networks. The process of modeling need no internal information of the harmonic source. The performance of the model is, for different configurations of the harmonic source, compared to the performance of other harmonic models. The results show that the proposed model has higher accuracy and is more suitable for practical power system. [ABSTRACT FROM AUTHOR]

In this paper, a chaotic three dimansional dynamical system is proposed, that is a modification of the system in Volos et al. (2017). The new system has two hyperbolic sine nonlinear terms, as opposed to the original system that only included one, in order to optimize system’s chaotic behavior, which is confirmed by the calculation of the maximal Lyapunov exponents and Kaplan-Yorke dimension. The system is experimentally realized, using Bi-color LEDs to emulate the hyperbolic sine functions. An extended dynamical analysis is then performed, by computing numerically the system’s bifurcation and continuation diagrams, Lyapunov exponents and phase portraits, and comparing the numerical simulations with the circuit simulations. A series of interesting phenomena are unmasked, like period doubling route to chaos, coexisting attractors and antimonotonicity, which are all verified from the circuit realization of the system. Hence, the circuit setup accurately emulates the chaotic dynamics of the proposed system.

In this paper, a significantly efficient time-domain algorithm is presented to analyze a transmission line, loaded by a nonlinear component and driven by an arbitrary modulated signal. The proposed method provides the envelope of the solution and removes the redundancy of the calculations. The efficiency of this method is achieved in two major steps. First, an unconditionally stable algorithm for the nonlinear circuit is introduced; The derived equations are generated based on the finite-difference time-domain technique and the results are confirmed by those of the Leapfrog method. As the circuit is excited by a modulated signal, decreasing the computational time by using the unconditionally stable algorithm alone, is not practical. Therefore, in the second step, a new time-domain approach is presented and utilized simultaneously, based on separating the high and low frequency behavior of the modulated signal, which enables the advantage of unconditionally stable algorithm effectively. The accuracy of the presented method is confirmed by the Leapfrog algorithm. The comparisons from the given examples indicate that almost 99.97% of the CPU time is decreased by using the proposed method. [ABSTRACT FROM AUTHOR]

We introduce in this paper an equivalence notion for submersions U → ℝ , U open in ℝ 2 , which makes it possible to identify a smooth planar curve with a unique class of submersions. This idea, which extends to the nonlinear setting the construction of a dual projective space, provides a systematic way to handle global implicit descriptions of smooth planar curves. We then apply this framework to model nonlinear electrical devices as classes of equivalent functions. In this setting, linearization naturally accommodates incremental resistances (and other analogous notions) in homogeneous terms. This approach, combined with a projectively-weighted version of the matrix-tree theorem, makes it possible to formulate and address in great generality several problems in nonlinear circuit theory. In particular, we tackle unique solvability problems in resistive circuits, and discuss a general expression for the characteristic polynomial of dynamic circuits at equilibria. Previously known results, which were derived in the literature under unnecessarily restrictive working assumptions, are simply obtained here by using dehomogenization. Our results are shown to apply also to circuits with memristors. We finally present a detailed, graph-theoretic study of certain stationary bifurcations in nonlinear circuits using the formalism here introduced. [ABSTRACT FROM AUTHOR]

The possibility of generating ultrabroadband chaotic oscillations within a frequency range up to 60 GHz with a bipolar SiGe heterojunction transistor is demonstrated. The uppermost frequency of this range is determined by the cutoff frequency of the active generator element. Such a possibility appears after the generator structure is complemented with an additional nonlinear circuit, in which chaotic oscillations can be developed up to the aforementioned frequency. Some results of the experimental study of one generator configuration based on lumped elements are presented. [ABSTRACT FROM AUTHOR]

In this paper a novel 3-D nonlinear finance chaotic system consisting of two nonlinearities with negative saving term, which is called ‘dissaving’ is presented. The dynamical analysis of the proposed system confirms its complex dynamic behavior, which is studied by using wellknown simulation tools of nonlinear theory, such as the bifurcation diagram, Lyapunov exponents and phase portraits. Also, some interesting phenomena related with nonlinear theory are observed, such as route to chaos through a period doubling sequence and crisis phenomena. In addition, an interesting scheme of adaptive control of finance system’s behavior is presented. Furthermore, the novel nonlinear finance system is emulated by an electronic circuit and its dynamical behavior is studied by using the electronic simulation package Cadence OrCAD in order to confirm the feasibility of the theoretical model.

This article examines the features of circuits in order to determine the possibility of their use for controlling thyristors when building new, simple and reliable circuits for controlling boost voltage stabilizers. In ferroresonant circuits connected to a voltage source with a low internal resistance, with a certain combination of parameters, oscillations are excited at the fundamental frequency, the initial phase of which has a shift with respect to the phase of the applied voltage. Moreover, the phase of the excited oscillations depends on the magnitude of the applied emf.

Future radar transmitters will need to be able to quickly reconfigure their radio-frequency circuitry to change operating frequency and spectral output while maintaining high power-added efficiency (PAE). In this paper, fast tuning of a tunable-varactor matching network is demonstrated to optimize the PAE while meeting requirements on the adjacent-channel power ratio. The tunable varactor network, a first-level prototype of a tunable radar amplifier matching network, incurs nonlinear performance, providing possible challenges to measurement accuracy. To address the issue of nonlinearities while maintaining ability to quickly reconfigure, the tunable-varactor network is characterized at different input power levels to allow useful performance in its nonlinear regime. The power-dependent characterization is used in an algorithm for optimization of an amplifier's PAE, by looking up the matching network characterization performed at the power estimated to be output by the amplifier. Measurement results show that this characterization enhances the consistency of the optimized PAE. Using the tunable varactor network reduces the optimization time to one-fourth of the time required when using the algorithm with a traditional mechanical load-pull tuner. [ABSTRACT FROM AUTHOR]

Summary: Low power/area cytomorphic chips may be interfaced and ultimately implanted in the human body for cell‐sensing and cell‐control applications of the future. In such electronic platforms, it is crucial to accurately mimic the biological timescales and operate in real time. This paper proposes a methodology where slow nonlinear dynamical systems describing the behaviour of naturally encountered biological systems can be efficiently realised in hardware. To this end, as a case study, a low power and efficient digital Application‐Specific Integrated Circuit capable of emulating slow intracellular calcium dynamics with timescales reaching to seconds has been fabricated in the commercially available AMS 0.35 μm technology and compared with its analog counterpart. The fabricated chip occupies an area of 1.5 mm2 (excluding the area of the pads) and consumes 18.93 nW for each calcium unit from a power supply of 3.3 V. The presented cytomimetic topology follows closely the behaviour of its biological counterpart, exhibiting similar time‐domain calcium ions dynamics. Results show that the implemented design has the potential to speed up large–scale simulations of slow intracellular dynamics by sharing cellular units in real time. This paper proposes a methodology where slow nonlinear dynamical systems describing the behavior of naturally encountered biological systems can be efficiently realised in hardware. To this end, a low power and efficient digital ASIC capable of emulating slow intracellular calcium dynamics has been fabricated in the AMS 0.35 μm technology and compared with its analog counterpart. The fabricated chip occupies an area of 1.5 mm2 and consumes 18.93 nW for each calcium unit from a power supply of 3.3 V. [ABSTRACT FROM AUTHOR]

A wide bandwidth energy harvester is designed with the purpose of operation under multiple excitations, where the excitation frequencies are generally incommensurate and probably spectrally close to each other. Owing this wideness of bandwidth to the nonlinearity of the circuit escalates the jeopardy of chaotic behavior while the circuit is exposed to multiple energy sources. In this study, the recently introduced Duffing based energy harvester is analyzed under multiple excitations and finally, a safe margin is calculated to avoid tumultuous behaviors which may affect adjacent sensitive electrical systems. The mathematical analyses given in this paper can be generalized to other types of nonlinear resonators. [ABSTRACT FROM AUTHOR]

In this work, the case of coupling (bidirectional and unidirectional) between two identical nonlinear chaotic circuits via a linear resistor, is studied. The produced dynamical systems have different structure, in regard to other similar works, due to the choice of coupling nodes. As a circuit, a modification of the most well-known nonlinear circuit that can operate in a wide range of radiofrequencies, the Colpitts oscillator, is chosen. The simulation and the experimental results show a variety of dynamical phenomena, such as periodic, quasi-periodic and chaotic behaviors, as well as anti-phase and complete synchronization phenomena, depending on the value of the coupling coefficient.

In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The initial study in this paper is to analyze the phase portraits, the Lyapunov exponents, the Poincaré maps and the bifurcation diagrams. Moreover, some appropriate comparisons are made to contrast some of the existing results. Finally, the effectiveness of the bidirectional coupling scheme between two identical Jerk circuits in a secure communication system is presented in details. Finally, the simulation results are shown to demonstrate that the proposed method is correct and feasible

In this work the antimonotonicity phenomenon is experimentally investigated in the case of a driven nonlinear R-L-Diode circuit, with or without a DC bias voltage. The nominated electronic circuit is one of the simplest and extensively studied nonlinear circuits that can be made in breadboard. Due to this fact, this is not an introductory paper but focuses specifically to the study of how the frequency of the sinusoidal voltage source acts to the dynamical behavior of the circuit, using appropriate nonlinear tools such as the bifurcation diagram, phase portrait, return map and correlation dimension. Furthermore, except of the antimonotonicity, a number of other interesting phenomena related to chaos has also been observed. [ABSTRACT FROM AUTHOR]