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Adaptive network models arise when describing processes in a wide range of fields and are characterized by some specific effects. One of them is mixed dynamics, which is the third type of chaos in addition to the conservative and dissipative types. In this work, we consider a more complex type of connections between network elements—simplex, or higher-order adaptive interactions. Using numerical simulation methods, we analyze various characteristics of mixed dynamics and compare them with the case of pairwise couplings. We found that mixed dynamics in the case of simplex interactions is characterized by a very high similarity of a chaotic attractor to a chaotic repeller, as well as a stronger closeness of the sum of the Lyapunov exponents of the attractor and repeller to zero. This means that in the case of three elements, the conservative properties of the system are more pronounced than in the case of two. [ABSTRACT FROM AUTHOR]

Recent studies demonstrate that the reproduction of prey is suppressed by the fear of predators. However, it will not respond immediately to fear, but rather reduce after a time lag. We propose a diffusive predator-prey model incorporating fear response delay into prey reproduction. Detailed bifurcation analysis reveals that there are three different cases for the effect of the fear response delay on the system: it might have no effect, both stabilizing and destabilizing effect, or destabilizing effect on the stability of the positive equilibrium, respectively, which are found by numerical simulations to correspond to low, intermediate or high level of fear. For the second case, through ordering the critical values of Hopf bifurcation, we prove the existence of stability switches for the system. Double Hopf bifurcation analysis is carried out to better understand how the fear level and delay jointly affect the system dynamics. Using the normal form method and center manifold theory, we derive the normal form of double Hopf bifurcation, and obtain bifurcation sets around double Hopf bifurcation points, from which all the dynamical behaviors can be explored, including periodic solutions, quasi-periodic solutions and even chaotic phenomenon. [ABSTRACT FROM AUTHOR]

An analytical classification in a three-dimensional parameter space is presented to describe the dynamics for an extended Lorenz system of the Li-Ou type, conditions are given to find supercritical and degenerate Hopf bifurcations and a pitchfork bifurcation. Finally, the theoretical results are compared with numerical simulations and bifurcation diagrams. [ABSTRACT FROM AUTHOR]

We investigate a discrete-time Chen system. First, we give the topological classifications of the fixed points of this system. Then, we analytically show that the discrete Chen system underlies a Neimark–Sacker (NS) bifurcation and period doubling (PD) under specific parametric circumstances. We confirm the existence of a PD and NS bifurcation via the explicit PD-NS bifurcation criterion and determine the direction of both bifurcations with the help of center manifold theory. We performed numerical simulations to confirm our analytical results. Furthermore, we use the 0-1 chaos test to quantify whether there is chaos in the system or not. At the end, the hybrid control strategy and the OGY (Ott, Grebogi, and Yorke) method are applied to eliminate chaotic trajectories of the system. [ABSTRACT FROM AUTHOR]

In this work. we consider an eco-epidemiological model with disease in prey. The role of alternative food is being investigated. Alternative food source for predator is another significant component in the interaction of ecological species and incorporation of this aspect in eco-epidemiological investigations may give some fascinating outcomes. The contribution of this paper is to consider different competition coefficients within the prey population. which leads to the emergent carrying capacity. The pernianence and uniform persistence are established. Moreover. we discuss the local and global stability analysis. For bifurcation analysis. the transmission rate has been taken as parameter. The Hopf bifurcation analysis around the endemic equilibrium point is discussed. Further. we also pay attention to the chaotic dynamics which is produced by the disease. At the end. extensive numerical simulations are performed to demonstrate the effectiveness of our hypothetical outcomes. The numerical simulations reveal that the three species eco-epidemiological system induced chaos when disease spreads iii low level. If we increase the force of infection. then the system shows stable focus through chaos to period-double. period-double to limit cycle. We conclude that chaotic dynamics can be coiitrolled by the alternative food as well as the competition coefficients. [ABSTRACT FROM AUTHOR]

At present, stochastic resonance (SR) based on Duffing and Langevin equations has been widely studied, but there is little research on SR phenomenon in higher-dimensional fractional-order systems. Based on the fractional-order Lorenz-like system, the SR phenomenon is studied from the perspective of equilibrium point in this paper. The dynamic process of SR phenomenon is presented, and several key parameters are derived. The results of numerical simulation show that the boundary of SR and chaos system will be broken if the order of the fractional-order system or internal parameters is properly adjusted, and the effect of SR phenomenon will also be influenced. This paper connects two important nonlinear phenomena (chaos and SR) based on the fractional-order system, which provides a new idea for the conversion between chaos and SR systems. [ABSTRACT FROM AUTHOR]

Regarding a nonlinear Zener model with a viscoelastic Maxwell element as the research object, the complicated dynamic behaviors such as homoclinic bifurcation and chaos under harmonic excitation are investigated. At first, the analytically necessary condition for chaos in the sense of Smale horseshoe is derived based on the Melnikov method. Then, the system parameters that meet the analytical condition and the main resonance condition are selected for the numerical simulation. From the bifurcation diagrams and the largest Lyapunov exponents, it is found that the homoclinic orbit breaks, and the system goes to chaos in a crisis way when the excitation amplitude passes the first threshold. The system enters another new chaotic state in the form of period-doubling bifurcation with the increase of the excitation amplitude. At last, the effects of nonlinear term, stiffness coefficient and damping coefficient of Maxwell element on the analytically necessary condition for chaos are analyzed, respectively, and the correctness of the analytical result is proved by numerical simulation. The research result shows that the critical excitation amplitude decreases with the increase of nonlinear term. In addition, the chaotic threshold increases first and then tends to remain unchanged with the raise of stiffness coefficient. The chaotic threshold increases first and then decreases with the enhancement of damping. These results provide a theoretical basis for the research of nonlinear viscoelastic system in the future. [ABSTRACT FROM AUTHOR]

In this paper, the bifurcation and chaotic motion of a piecewise Duffing oscillator with delayed displacement feedback under harmonic excitation are studied. Based on the Melnikov method, the necessary critical conditions for the chaotic motion in the system are obtained, and the chaos threshold curve is obtained by calculation and numerical simulation. The accuracy of the analytical result is proved by some typical numerical simulation results, including the local bifurcation diagrams, phase portraits, Poincaré maps, and the largest Lyapunov exponents. The effects of excitation frequency and time delay of the displacement feedback are analytically discussed. It could be found that the critical excitation amplitude will increase obviously with the increase of the excitation frequency, and under the selection of certain parameters, the critical excitation amplitude takes the time delay of 0.58 as the inflection point, which decreases at first and then increases. [ABSTRACT FROM AUTHOR]

In this paper, we study a dual-channel closed-loop supply chain (CLSC) consisting of one manufacturer, one retailer and one third-party firm or platform (3P). The manufacturer wholesales new products through the traditional retail channel and distributes remanufactured products via 3P. We focus on establishing the dynamic Stackelberg game models for nondelayed and delayed cases, respectively. The existence and local stability of Nash equilibrium are examined as well as the complex dynamical behaviors of each model under various scenarios are investigated by numerical simulations, such as stability region, bifurcations, chaos, strange attractors, and so on. Moreover, the impacts of some key parameters on the performance of chain members are analyzed. In addition, the variable feedback control method is utilized to eliminate the system chaos. The results reveal that the high value of the consumer discount perception for remanufactured products and excessively fast price adjustment speed have a destabilization effect on the Nash equilibrium point. In addition, adopting delay decisions by manufacturer does not always make the system more stable because it can exert either positive or negative effect on the system's stability, while an intermediate delay weight is conducive to the system have a higher chance to stay stable. Furthermore, the manufacturer's profits will be declined significantly while the profits of retailer and 3P will be elevated to some extent when the system falls into periodic and chaotic motions, so chaos is not always necessarily detrimental to all the decision makers in the dual-channel CLSC. [ABSTRACT FROM AUTHOR]

The classical approach to analyze pharmacokinetic (PK) data in bioequivalence studies aiming to compare two different formulations is to perform noncompartmental analysis (NCA) followed by two one-sided tests (TOST). In this regard, the PK parameters area under the curve (AUC) and $C_{\max}$ are obtained for both treatment groups and their geometric mean ratios are considered. According to current guidelines by the U.S. Food and Drug Administration and the European Medicines Agency, the formulations are declared to be sufficiently similar if the $90\%$ confidence interval for these ratios falls between $0.8$ and $1.25 $. As NCA is not a reliable approach in case of sparse designs, a model-based alternative has already been proposed for the estimation of $\rm AUC$ and $C_{\max}$ using nonlinear mixed effects models. Here we propose another, more powerful test than the TOST and demonstrate its superiority through a simulation study both for NCA and model-based approaches. For products with high variability on PK parameters, this method appears to have closer type I errors to the conventionally accepted significance level of $0.05$, suggesting its potential use in situations where conventional bioequivalence analysis is not applicable. [ABSTRACT FROM AUTHOR]

In recent years, encryption technology has been developed rapidly and many image encryption methods have been put forward. The chaos-based image encryption technique is a modern encryption system for images. To encrypt images, it uses random sequence chaos, which is an efficient way to solve the intractable problem of simple and highly protected image encryption. There are, however, some shortcomings in the technique of chaos-based image encryption, such limited accuracy issue. The approach focused on the chaotic system in this paper is to construct a dynamic IP permutation and S-Box substitution by following steps. First of all, use of a new IP table for more diffusion of all image pixels based on a 1D logistic map to build IP table. Secondly, a new S-Box based on 2D-Henon chaos was created using more confusion to replace G-channel image data. Finally, design of a modern image encryption approach. This approach uses the key process confusion and diffusion operation and depend on IP and S-Box proposals in the encryption process and several shuffling operations using the 3D- Lornez chaos theory. Theoretical research and simulation suggest that starting sensitivity value of this method is high, has high protection, and encryption speed. Moreover, it also holds the value of the neighboring RGB close to zero. The studies show that the information security capabilities would be both safer and more efficient, as a result of our image quality assessment study. Number of Differential Pixel Rate Change Attacks (NPSR), Unified Average Altered Intensity (UACI), are quality and strength of encryption processing are proved by pixel correlation, Entropy to be good results. [ABSTRACT FROM AUTHOR]

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting. [ABSTRACT FROM AUTHOR]

In this paper, a simple chaotic memristor-based circuit with an external stimulation is proposed, and its basic dynamic properties are demonstrated. When the external perturbation becomes time varying and its frequency is low enough, the system has two-time scales, which can be employed to explore the mechanisms of symmetrical Hopf-induced bursting oscillations and delay effects. Furthermore, delay-times on Hopf-induced bursting at different frequencies of the external stimulation are measured. The results show that the relationship between the delay-time and external frequency is subject to a power law. In order to enhance the existing chaos of the system, a 4D system is developed by adding a nonlinear state feedback controller, which shows hyperchaos under some suitable parameters. These two systems are implemented on Multisim and hardware platforms, and the corresponding experimental results verify the correctness of the numerical simulations. [ABSTRACT FROM AUTHOR]

• Perceptual development evolves in a stereotyped manner, from limited to proficient. • Here, we focus on the functional significance of such developmental progressions. • We review empirical and computational studies of typical and atypical development. • Early perceptual limitations have therein emerged as scaffolds rather than hurdles. • Thus, the developmental sequencing from limited to proficient may be adaptive. Human perceptual development evolves in a stereotyped fashion, with initially limited perceptual capabilities maturing over the months or years following the commencement of sensory experience into robust proficiencies. This review focuses on the functional significance of these developmental progressions. Specifically, we review findings from studies of children who have experienced alterations of early development, as well as results from corresponding computational models, which have recently provided compelling evidence that specific attributes of early sensory experience are likely to be important prerequisites for later developing skills in several perceptual domains such as vision and audition. Notably, the limitations of early sensory experience have therein emerged as scaffolds, rather than hurdles, being causally responsible for the acquisition of later perceptual proficiencies, while dispensing with these limitations has the perhaps counter-intuitive consequence of compromising later development. These results have implications for understanding why normal trajectories of perceptual development are sequenced in the way that they are, help account for the perceptual deficits observed in individuals with atypical histories of sensory development, and serve as guidelines for the creation of more robust and effective training procedures for computational learning systems. [ABSTRACT FROM AUTHOR]

A chaotic parameter-optimized radial basis function (RBF) forecasting model was proposed. The chaos theory was used to obtain the embedded dimension and delay time of the ENPEMF， and the obtained parameters were used to optimize the RBF neural network. Finally， the trained optimized-RBF was utilized to forecast the strength trend of 14 d ENPEMF data. Numerical simulation results show that the improved RBF model could forecast the Rossler time series well with small error. Applying the improved RBF algorithm to the ENPEMF data before Ms7.0 earthquake in Lushan， it can effectively forecast the ENPEMF intensity trend 14 d before earthquake. The forecasting effect and accuracy are significantly better than that of the traditional RBF algorithm， which is expected to provide support for electromagnetic monitoring and analysis before earthquakes and geological disasters. [ABSTRACT FROM AUTHOR]

In this paper, a novel chaotic new three-dimensional system has been studied by Zhang et al. in 2012. In the system, there are three control parameters and three different nonlinear terms which governed equations. Zhang et al. studied elementary (preliminary) dynamic properties of the chaotic new three-dimensional system by means of bifurcation diagram, maximum Lyapunov exponent, phase portraits, dynamics behaviors by changing some parameters etc., using all possible theoretical analysis and numerical simulation. In this paper, we have demonstrated its complete synchronization. The proposed results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamical behaviors of a duopoly model with two content providers (CPs). Competition between two CPs is assumed to take place in terms of their pricing decisions and the credibility of content they offer. According to the CPs' rationality level, we consider a scenario where both CPs are bounded rational. Each CP in any period uses the marginal profit observed from the previous period to choose its strategies. We compute explicitly the steady states of the dynamical system induced by bounded rationality, and establish a necessary and sufficient condition for stability of its Nash equilibrium (NE). Numerical simulations show that if some parameters of the model are varied, the stability of the NE point is lost and the complex (periodic or chaotic) behavior occurs. The chaotic behavior of the system is stabilized on the NE point by applying control. [ABSTRACT FROM AUTHOR]

In this paper, computer assisted proofs in dynamics (CAPD) group and conventional dynamic analysis methods are applied to find the parameters that make the brushless DC motor (BLDCM) system chaotic. For the purpose to make the BLDCM system exponentially stable, four simple controllers with just one state variable are proposed, which means that it only needs one sensor instead of two or more in practice. Numerical simulations show that the motor with the new controllers can converge efficiently. Finally, the topological horseshoe theory is introduced to verify the existence of chaos in BLDCM system. [ABSTRACT FROM AUTHOR]

Highlights • DNA encoding is introduced into the field of optical encryption. • An optical XOR gate is used to achieve XOR operation in ultra-fast DNA encryption. • The DNA rules used for data encoding are different in each row and column, which enhances the security of system. Abstract We propose an optical image encryption scheme based on the Deoxyribonucleic Acid (DNA) theory and the double random phase encoding (DRPE) technique. The piecewise linear chaotic map (PWLCM) is used to generate key images and random phase masks, and to determine DNA encoding rules. In order to achieve ultra-fast DNA encryption, we propose using an optical exclusive-OR (XOR) gate to achieve XOR operation in DNA encryption. Different plaintexts use different initial values of PWLCM, which are generated by Message Digest Algorithm 5 (MD5). The plaintext is encrypted by two rounds of DNA and then by DRPE to form a ciphertext. Numerical simulation and the analysis of attacks on encrypted image are implemented to demonstrate the security and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract In this work, we further investigate the dynamics of the Genesio-Tesi chaotic system which consists of a relatively simple jerk circuit with a quadratic nonlinearity. We complete and enrich the results obtained by Aceng et al. (2016). For this reason, we focus our interest in multistability generation and chaos synchronization as well. By using simulation software tools like PASCAL compiler, Orcad PSPICE and MATLAB, these properties have been characterized via common nonlinear tools including phase portraits, temporal responses, frequency responses, bifurcation diagrams and maximum lyapunov exponent plots. The analysis shows that the Genesio-Tesi system under consideration is able to exhibit complex and interesting behaviors including period doubling bifurcation, chaos, periodic windows and coexistence of multiple attractors. This latter phenomenon has not been found in previous studies of the Genesio-Tesi oscillator thus merits to be shared. We have also shown that Genesio-Tesi systems in their chaotic states can be synchronized and used for a possible masking of information, thus illustrating its importance in engineering. Numerical findings have been validated through experimental studies. [ABSTRACT FROM AUTHOR]

Bifurcations in Huang's chaotic chemical reactor leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales, and its stability is determined from the resulting normal form and verified by numerical simulations. The dynamically rich range of parameters past the Hopf bifurcation is next explored. In order to bring some order to the search for parameter regimes with more complex dynamics, we employ the recent conjecture of Competitive Modes to find chaotic parameter sets in the large multiparameter space for this system. In addition, it is demonstrated that, by changing the point of view, one may tightly localize the chaotic attractor in shape and location in the phase space by mapping the Competitive Modes surfaces geometrically. Finally, we consider the effect of delay on the system, leading to the suppression of the Hopf bifurcation in some regimes, and also all of the subsequent complex dynamics. In modern terminology, this is an example of Amplitude Death, rather than Oscillation Death, as the complex system dynamics is quenched, with all the variables additionally settling to a fixed point of the original system. [ABSTRACT FROM AUTHOR]

Abstract As for the dynamical networks which consist of some high-dimensional nonlinear systems, the problems that researchers are concerned with are usually the asymptotic convergence on some components (rather than all components) of node's state variables under certain condition. This means that partial component synchronization is more meaningful than identical synchronization in some cases. In this paper, the definition of partial component synchronization is given, and then the problem of partial component synchronization on a class of chaotic dynamical networks is investigated. By using matrix theory, stability theory and the hypothesis that several components in the solution vector of a single uncoupled node are ultimately dissipative, some sufficient conditions on partial component synchronization in the chaotic dynamical networks are derived. Finally, numerical simulations are shown to demonstrate the correctness of the theoretical results. Highlights • Partial component synchronization is a kind of group dynamics behavior weaker than identical synchronization. • In this paper, the definition of partial component synchronization is given, and the stability theory of partial variables is applied to study it. • Several sufficient conditions for partial component synchronization to be realized on the network are derived. [ABSTRACT FROM AUTHOR]

Abstract The Rulkov mapping is a phenomenological model that simulates the changes in the neuronal membrane potential. In this work, we introduce a parametric perturbation in the Rulkov map, that can be related to an unexpected behavior, such as a malfunction of the neuronal membrane due to pathologies. The perturbed system still keeps its main characteristics, which includes periodic behavior followed by chaotic bursts. We verify the existence of a set of periodic regions, known as shrimps, embedded in chaotic attractors in the system with parametric perturbation. Some changes in the phase space, time evolution of the variables and bifurcation diagrams are observed. Finally, we show the extreming curves, which demonstrate how is the organization of the periodic regions in the parameter space. Highlights • Parametric perturbation in the Rulkov mapping. • A model that describes the neuronal membrane potential is studied. • The system presents periodic behavior followed by chaotic bursts. • We show how is the organization of the periodic regions in the parameter space. [ABSTRACT FROM AUTHOR]

In this paper, a Noval chaotic dynamical system is proposed and the basic properties of the system are investigated. Linear feedback control technique is used to suppress chaos. The controlled system is stable under some conditions on the parameters of the system determined by Lyapunov direct method. In addition, a function projective synchronization of two identical Noval system is presented. Lyapunov method of stability is used to prove the asymptotic stability of solutions for the error dynamical system. Numerical simulations results are included to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

In this paper, analytical solutions of periodic evolutions of the Brusselator with a harmonic diffusion are obtained through the generalized harmonic balance method. The stability and bifurcation of the periodic evolutions are determined. The bifurcation tree of period-1 to period-8 evolutions of the Brusselator is presented through frequency-amplitude characteristics. To illustrate the accuracy of the analytical periodic evolutions of the Brusselator, numerical simulations of the stable period-1 to period-8 evolutions are completed. The harmonic amplitude spectrums are presented for the accuracy of the analytical periodic evolution, and each harmonics contribution on the specific periodic evolution can be achieved. This study gives a better understanding of periodic evolutions to chaos in the slowly varying Brusselator system, and the bifurcation tree of period-1 evolution to chaos are clearly demonstrated, which can help one understand a route of periodic evolution to chaos in chemical reaction oscillators. From this study, the generalized harmonic balance method is a good method for slowly varying systems, and such a method provides very accurate solutions of periodic motions in such nonlinear systems. [ABSTRACT FROM AUTHOR]

Abstract In order to detect rail cracks by Acoustic Emission (AE) technology, many researches are carried out based on the theoretical and experimental conditions. However, how to detect the crack signals in real noise environment of railway is a key problem for actual application, which has few researches. In this paper, AE detection of rail cracks in real noise environment is investigated and an improved method is proposed to increase the accuracy of crack detection. The AE noise signals are acquired from real operation conditions. They are analyzed and reconstructed by chaos theory. Based on the reconstructed vectors, a reasonable Nonlinear AutoRegressive with eXogenous input (NARX) model of AE noises is built to eliminate noises. For suppressing the abnormal noise interference, a feature detection method is proposed to improve the detection accuracy based on the fused features. Meanwhile, the detection ability of the proposed method is further verified by a longer signal. The results illustrate that the proposed method is effective to detect crack signals in real noise environment. Moreover, the actual application of the proposed method is also discussed and it can provide a useful guidance for AE detection of rail cracks. Highlights • AE detection of rail crack is investigated in real noise environment of railway. • An improved method is proposed to increase the detection accuracy of crack signal. • Generation system of simulated crack signal is designed for nondestructive research. • NARX model is built to eliminate normal AE noises by Chaos theory. • The fused features are employed to suppress abnormal AE noises. [ABSTRACT FROM AUTHOR]

A chaos particle swarm optimization (CPSO) algorithm based on the chaos operator (CS) is proposed for global optimization problems and parameter inversion of the nonlinear sun shadow model in our study. The CPSO algorithm combines the local search ability of CS and the global search ability of PSO algorithm. The CPSO algorithm can not only solve the global optimization problems effectively, but also address the parameter inversion problems of the date of sun shadow model location successfully. The results of numerical experiment and simulation experiment show that the CPSO algorithm has higher accuracy and faster convergence than the-state-of-the-art techniques. It can effectively improve the computing accuracy and computing efficiency of the global optimization problems, and also provide a novel method to solve the problems of integer parameter inversion in real life. [ABSTRACT FROM AUTHOR]

This article deals with the dynamical analysis of discrete-time Brusselator models. Euler’s forward and nonstandard difference schemes are implemented for discretization of Brusselator system. We investigate the local dynamics related to equilibria of both discrete-time models. Furthermore, with the help of bifurcation theory and center manifold theorem, explicit parametric conditions for directions and existence of flip and Hopf bifurcations are investigated. A novel chaos control method is implemented in order to control chaos in discrete-time Brusselator models under the influence of flip and Hopf bifurcations. Numerical simulations are provided to illustrate theoretical discussion and effectiveness of newly introduced chaos control strategy. [ABSTRACT FROM AUTHOR]

In this work, we aimed to solve the control regulation problem for a generalized second-order underactuated linear system in order to induce a periodic or chaotic behavior or to cancel the external perturbations, generated by an exogenous system, in the nonactuated coordinate. Further, we showed that, in some cases, it is possible to bring to zero the regulation output errors of the underactuated linear plant, depending on the structure of the plant itself and the exogenous system. In the first stage, the solution was developed for the ideal scenario, in which the whole states of the plant and of the exogenous system were available. Secondly, we showed that in some cases it was possible to solve the regulation output problem when only the observable plant output was measurable. That is, the whole plant state and the exogenous signal could be recovered, if some assumptions were fulfilled. The Lyapunov method was used to perform the stability analysis. The proposed solution was assessed through numerical simulations. [ABSTRACT FROM AUTHOR]

This paper puts forward the control of chaos in the biological system. A new controller based on recursive backstepping sliding mode control is proposed such that it can control the chaotic dynamics in the biological system to stabilize at any position or to track any trajectory that is a smooth function of time. A proportional integral switching surface is proposed to achieve the stability condition of the error dynamics. Unlike the open loop and open plus closed loop control techniques, the design of proposed controller does not require the parameter perturbation. The required stability condition is derived based on Lyapunov stability theory. Simulation is achieved in MATLAB environment. Numerical simulation results are presented in order to show the effective verification of the proposed controller design. Simulation results correspond that the objective of chaos control is achieved successfully. [ABSTRACT FROM AUTHOR]

A diagnostic technique is proposed for the mode of generalized synchronization in systems with a complex chaotic attractor topology based on consideration of tubes of trajectories in the phase space of interacting systems. The method functionality is tested by the numerical simulation of two mutually coupled modified Lorentz systems: one in the chaotic state, and another in the hyperchaotic state. The results are compared to the data obtained by calculating the Lyapunov exponent spectrum and show good agreement. [ABSTRACT FROM AUTHOR]

Chaotic and regular behavior of the system consisting of a double physical pendulum with two repulsive permanent magnets is studied. We are focused on mathematical modelling, numerical simulations, experimental measurements and in particular on a novel magnetic interaction modelling. System parameters are identified by matching the output signals from experiments and numerical solutions to the developed mathematical model governed by a strongly non-linear set of two second order ODEs including the friction and the magnetic interaction torques. Considered system shows chaotic and periodic dynamics. Few chaotic zones have been detected numerically and confirmed experimentally. Scenarios of transition from regular to chaotic motion and vice versa, as well as the bifurcation diagrams are illustrated and discussed. Good agreement between the numerical simulation and experimental measurement is achieved. [ABSTRACT FROM AUTHOR]

This theoretical work considers the following conundrum: linear response theory is successfully used by scientists in numerous fields, but mathematicians have shown that typical low-dimensional dynamical systems violate the theory’s assumptions. Here we provide a proof of concept for the validity of linear response theory in high-dimensional deterministic systems for large-scale observables. We introduce an exemplary model in which observables of resolved degrees of freedom are weakly coupled to a large, inhomogeneous collection of unresolved chaotic degrees of freedom. By employing statistical limit laws we give conditions under which such systems obey linear response theory even if all the degrees of freedom individually violate linear response. We corroborate our result with numerical simulations. [ABSTRACT FROM AUTHOR]

Different from previous works on chaotic synchronization of fractional-order system, this paper discusses the chaotic synchronization of Lorenz system with distributed order. The main idea is that we transform the distributed-order Lorenz system in the time domain into the frequency domain by Laplace transformation, and then, based on the final-value theorem, two main theorems and the designed controllers, the chaotic synchronization between the distributed-order Lorenz drive system and response system is obtained. Finally, numerical simulations and applications in chaotic masking are presented to verify reliability of the obtained results. [ABSTRACT FROM AUTHOR]

Results of investigation of regular and chaotic motions of near-Earth asteroids (NEAs) in the vicinity of the 1:2 mean motion resonance with the Earth and 2:1 mean motion resonance with Jupiter are discussed in the present work. The resonant zones, constructed from the set of initial values of the semimajor axis and the mean anomaly at some fixed values of other orbital elements, are numerically simulated. By means of the MEGNO parameter, the vicinities of the boundaries of these zones are investigated. Chaotic zones are represented graphically, and the widths of these zones are numerically estimated. The behavior of the resonant and chaotic zones is demonstrated for different values of the eccentricity and inclination. [ABSTRACT FROM AUTHOR]

In this paper synchronization of fractional–order Liu chaotic oscillators is addressed. Two networks of fractional–order Liu chaotic oscillators are synchronized by appealing to results from complex systems theory for integer–order systems. We use and implement complex dynamical networks composed by nine Liu chaotic oscillators. Two scenarios are considered: (i) complex network with regular topology, and (ii) complex network with irregular topology. Synchronization of both complex networks is achieved by coupling the fractional–order chaotic oscillators through their second state. We use numerical simulations to verify the results, we also show an FPGA realization of the complex networks previously synchronized. [ABSTRACT FROM AUTHOR]

Background: ALZ-801 is an oral, small-molecule inhibitor of beta amyloid (Aβ) oligomer formation in clinical development for Alzheimer's disease (AD). ALZ-801 is a prodrug of tramiprosate with improved pharmacokinetic properties and gastrointestinal tolerability. During clinical studies, we discovered that the primary metabolite of tramiprosate and its prodrug ALZ-801, 3-sulfopropanoic acid (3-SPA), is an endogenous molecule in the human brain and present in the cerebrospinal fluid (CSF) of patients with AD and other neurodegenerative brain diseases.Objective: The objectives of this research were to (1) identify and confirm the presence of 3-SPA in CSF samples from elderly, drug-naïve patients with memory deficits; (2) quantify the levels of 3-SPA in the CSF of patients with AD from tramiprosate phase III North American (NA) trial; (3) evaluate the in vitro anti-Aβ42 oligomer activity of 3-SPA; and (4) characterize the pharmacokinetics and brain-penetration properties of 3-SPA.Methods: Lumbar CSF samples from 64 drug-naïve patients with cognitive deficits (Mini-Mental State Examination [MMSE] score range 15-30) and six patients with AD treated with tramiprosate 150 mg twice daily in the phase III trial, at week 78, were analyzed. We used liquid chromatography-tandem mass spectrometry to confirm the structural molecular identity of endogenous 3-SPA with a 3-SPA reference standard and ion-mobility spectrometry-mass spectrometry with molecular dynamics to characterize interactions of 3-SPA with Aβ42 monomers, and the resultant conformational alterations. Rat studies using oral (30 mg/kg) and intravenous (10 mg/kg) doses were conducted to characterize the pharmacokinetic properties and brain penetration of 3-SPA.Results: We confirmed the presence of 3-SPA in the CSF of drug-naïve patients with cognitive deficits (mean concentration 11.7 ± 4.3 nM). The mean concentration of 3-SPA in patients with AD treated with tramiprosate was 135 ± 51 nM. In vitro studies revealed a multi-ligand interaction of 3-SPA with monomeric Aβ42 that inhibits the aggregation of Aβ42 into small oligomers. Comparisons of the molecular interactions of tramiprosate and 3-SPA with Aβ42 are also presented. Furthermore, in rat preclinical studies, 3-SPA displayed 100% oral bioavailability and 25% brain penetration, indicating that the metabolite is well absorbed and crosses the blood-brain barrier.Conclusions: We confirmed the endogenous presence of 3-SPA, the major metabolite of tramiprosate, in the CSF of drug-naïve elderly patients with memory deficits due to AD and a variety of other neurodegenerative disorders. The levels of 3-SPA were up to 12.6-fold greater in patients with AD receiving tramiprosate than in drug-naïve patients. In addition, we showed that 3-SPA has potent anti-Aβ oligomer activity, inhibiting aggregation of Aβ42 into small oligomers with efficacy comparable to that of tramiprosate. 3-SPA displays excellent oral availability and brain penetration in rats, suggesting that the higher CSF concentrations of 3-SPA in the human brain after oral administration of ALZ-801 or tramiprosate (and subsequent conversion to 3-SPA) result from the penetration of the metabolite into the central nervous system. These data suggest that 3-SPA is an endogenous agent with potential activity stabilizing the conformational flexibility of Aβ monomers that, in turn, inhibit Aβ misfolding and formation of soluble toxic Aβ oligomers in humans, thereby preventing the initial pathogenic step in the progression of AD. Clinical improvements observed in patients with AD carrying the ε4 allele of the apolipoprotein E gene in tramiprosate phase III studies may in part be explained by the therapeutic effects of excess levels of the metabolite in the brains of these patients. The potential protective role of 3-SPA in AD pathogenesis, as well as its therapeutic role in AD and other neurodegenerative disorders, warrants further investigation. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the dynamics of a fourth-order normal form near a double Takens-Bogdanov bifurcation. The reduced system of this normal form possesses eight pairs of homoclinic orbits for certain parameter values. The nonlinear time transformation method is applied to obtain an analytical approximation of the homoclinic orbit in the perturbed system and to construct the homoclinic bifurcation curve as well. Using numerical continuation, period-doubling and homoclinic-doubling cascades emanating from a codimension-2 bifurcation point are found. A codimension-2 homoclinic-gluing bifurcation point at which several homoclinic orbits concerning the origin glue together to form a new homoclinic orbit is also obtained. It is shown that in the vicinity of these bifurcation points, the system may exhibit chaos and chaotic attractors. [ABSTRACT FROM AUTHOR]

In this brief communication, Melnikov’s method is adopted to investigate the chaotic behaviors of a nanoplate postulating nonlinear Winkler foundation. The critical curves separating the chaotic and non-chaotic regions are found. It is presented that the chaotic behaviors can occur when the parameters are chosen in the chaotic regions. Numerical simulations verify the theoretical analytical results. The results provide some inspiration and guidance for the analysis and dynamic design of this nanoplate. [ABSTRACT FROM AUTHOR]

The transition to a chaotic plume from a two-dimensional (2D) open cavity heated from below has been investigated using numerical simulation. A large range of Rayleigh numbers (Ra) pertaining to an aspect ratio of A = 1, and Prandtl number (Pr) of Pr = 0.71 (air) is numerically investigated. It is shown that there exists a complex transition of the plume from a steady reflection symmetry to a chaotic flow with a sequence of bifurcations. As the Rayleigh number increases, the plume from the open cavity undergoes a supercritical pitchfork bifurcation from a steady reflection symmetry to a steady reflection asymmetry flow. Once the Rayleigh number exceeds 7 × 10 3 , the plume appears as a distinct flapping namely, a Hopf bifurcation, and then as a distinct puffing. The chaotic plume has the possibility to exhibit an alternate appearance of flapping and puffing in the event the Rayleigh number exceeds 8 × 10 4 . Moreover, the dynamics of the plume from the open cavity is discussed, and the dependence on the Rayleigh number of heat and mass transfer of the plume from the open cavity is quantified. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive robust finite-time control method based on a global sliding surface for the synchronization of a class of chaotic systems. New chattering-free control laws are designed to guarantee the removal of the reaching mode and realize the existence of the sliding mode around the designed surface right from the first moment. The proposed adaptive-tuning controllers eliminate the requirement of knowledge about disturbance bounds. Using the suggested control technique, superior master–slave synchronization is achieved, the chattering problem is fully solved, and the amplitudes of the control signals are noticeably decreased. Demonstrative simulation results for a Lü chaotic system are presented to indicate the efficiency and usefulness of the proposed scheme. In the end, using a state-feedback controller, we obtain a four-dimensional system with two interesting features. First, some hyperchaotic solutions are proposed, and then a continuous bifurcation diagram showing chaos for a wide range of bifurcation parameter is presented. [ABSTRACT FROM AUTHOR]

Little seems to be known about the chaotification control of fractional order linear and nonlinear systems. This paper proposes a novel chaotification method for fractional order nonlinear systems based on the negative damping instability mechanism and fractional calculus technique. We then apply it to chaotify the fractional order Lorenz system with order lying in ( 1 , 2 ) , which is stable originally with specific parameters. Moreover, we introduce three critical effective orders to distinguish different four dynamics: singleton sets attractor, self-excited attractor, coexisting attractors, and blow up behavior. Many simulations are carried out to illustrate the effectiveness of the results. [ABSTRACT FROM AUTHOR]

Nowadays various chaotic secure communication systems based on synchronization of chaotic circuits are widely studied. To achieve synchronization, the control signal proportional to the difference between the circuits signals, adjust the state of one circuit. In this paper the synchronization of two Chua circuits is simulated in Simulation Programs with Integrated Circuit Emphasis. It is shown that the choice of control signal is not straightforward, especially in the case of multistability and hidden attractors. [ABSTRACT FROM AUTHOR]

Cas scaffolding protein family member 4 and protein tyrosine kinase 2 are signaling proteins, which are involved in neuritic plaques burden, neurofibrillary tangles, and disruption of synaptic connections in Alzheimer's disease. In the current study, a computational approach was employed to explore the active binding sites of Cas scaffolding protein family member 4 and protein tyrosine kinase 2 proteins and their significant role in the activation of downstream signaling pathways. Sequential and structural analyses were performed on Cas scaffolding protein family member 4 and protein tyrosine kinase 2 to identify their core active binding sites. Molecular docking servers were used to predict the common interacting residues in both Cas scaffolding protein family member 4 and protein tyrosine kinase 2 and their involvement in Alzheimer's disease-mediated pathways. Furthermore, the results from molecular dynamic simulation experiment show the stability of targeted proteins. In addition, the generated root mean square deviations and fluctuations, solvent-accessible surface area, and gyration graphs also depict their backbone stability and compactness, respectively. A better understanding of CAS and their interconnected protein signaling cascade may help provide a treatment for Alzheimer's disease. Further, Cas scaffolding protein family member 4 could be used as a novel target for the treatment of Alzheimer's disease by inhibiting the protein tyrosine kinase 2 pathway. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive finite-time modified function projective lag synchronisation with definite attenuation rate for a class of chaotic systems with unknown parameters. Firstly, a novel integral type terminal sliding surface is proposed to ensure the finite-time stability of the sliding motion. Subsequently, an adaptive finite-time control law is designed to guarantee the occurrence of the sliding motion in a limited time and the accurate estimation of the unknown parameters. Moreover, the exponential attenuation rate designed in this paper can further cut down the synchronisation time. Numerical simulations are presented to verify the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The global synchronization of coupled neural networks with hybrid coupling has been studied in this paper. The hybrid coupling is formed from constant coupling, discrete-delay coupling, and distributed-delay coupling. In this regard, a larger class and more complicated coupled neural networks lead in the synchronization problem procedure. According to the new augmented Lyapunov-Krasovskii functional and the idea of M-segmentation of delay length, a less conservative delay-dependent criterion is obtained and expressed in the form of linear matrix inequalities. In many cases, due to the increasing segmentation number, the delay length M-segmentation method could give an opportunity to the user to find a bigger upper bound of the maximum allowable time delay. The effectiveness of suggested method above is proved by simulating a numerical example on a typical chaotic cellular neural network. The results show that the above-mentioned method is less conservative than the other methods reviewed in this article. [ABSTRACT FROM AUTHOR]

The second-order chaotic oscillation system model is used to analyze the dynamic behavior of chaotic oscillations in power system. To suppress chaos and stabilize voltage within bounded time independent of initial condition, an adaptive fixed-time fast terminal sliding mode chaos control strategy is proposed. Compared with the conventional fast terminal sliding mode control strategy and finite-time control strategy, the proposed scheme has advantages in terms of convergence time and maximum deviation. Finally, simulation results are given to demonstrate the effectiveness of the proposed control scheme and the superior performance. [ABSTRACT FROM AUTHOR]