Phenomenon Of Chaotic Synchronization Research Articles

Coupling of neurons favors the bursting behavior and the predominance of the tripod gait

In nature, it has been observed that the dominant locomotor pattern of hexapod insects is often the tripod gait. Our analysis of a Central Pattern Generator (CPG) of the insect movement gives reasons for this dominance: the mathematical CPG model presents the tripod pattern with bursting dynamics in a parametric region where an isolated neuron has a simpler behavior. That is, we show how the coupling of small networks of neurons makes the system to continue having bursting dynamics even when an isolated neuron would be spiking. Moreover, in parametric regions where a neuron shows chaotic dynamics, the CPG exhibits a chaotic synchronization phenomenon: the chaotic tripod gait. In other words, coupling loves bursting… and tripod gait. The hyperchaotic phenomenon is also present and we locate regions where up to four Lyapunov exponents are positive.

Multistability near the boundary of noise-induced synchronization in ensembles of uncoupled chaotic systems

The aim of this work is to study the possibility of the existence of multistability near the boundary of noise-induced synchronization in chaotic continuous and discrete systems. Ensembles of uncoupled Lorenz systems and logistic maps being under influence of a common source of white noise have been chosen as an object under study. Methods. The noise-induced synchronization regime detection has been performed by means of direct comparison of the system states being under influence of the common noise source and by calculation of the synchronization error. To determine the presence of multistability near the boundary of this regime, the multistability measure has been calculated and its dependence on the noise intensity has been obtained. In addition, for fixed moments of time, the basins of attraction of the synchronous and asynchronous regimes have been received for one of the systems driven by noise for fixed initial conditions of the other system. The result of the work is a proof of the presence of multistability near the boundary of noise-induced synchronization. Conclusion. It is shown that the regime of intermittent noise-induced synchronization, as well as the regime of intermittent generalized synchronization, is characterized by multistability, which manifests itself in this case as the existence in the same time interval of the synchronous behavior in one pair of systems being under influence of a common noise source, whereas in the other pair the asynchronous behavior is observed. The found effect is typical for both flow systems and discrete maps being under influence of a common noise source. It can find an application in the information and telecommunication systems for improvement the methods for secure information transmission based on the phenomenon of chaotic synchronization.

Analysis of the cooperative dynamics of nonlinear systems based on joint singularity spectrum

A generalization of the wavelet-transform modulus maxima method to the case of multifractal analysis is proposed, in which the cooperative dynamics of subsystems and the change in the interaction between them are characterized using a joint singularity spectrum. On the example of the phenomenon of chaotic synchronization in the model of interacting Lorenz systems, the possibility of diagnosing a change in the functioning regime in terms of the wavelet-based multifractal formalism is illustrated. Keywords: multifractal analysis, random process, scaling, singularity spectrum.

Анализ кооперативной динамики нелинейных систем на основе совместного спектра сингулярностей

A generalization of the wavelet-transform modulus maxima method to the case of multifractal analysis is proposed, in which the cooperative dynamics of subsystems and the change in the interaction between them are characterized using a joint singularity spectrum. On the example of the phenomenon of chaotic synchronization in the model of interacting Lorentz systems, the possibility of diagnosing a change in the functioning regime in terms of the wavelet-based multifractal formalism is illustrated.

Experimental chaotic synchronization for coupled double pendula.

10.1063/5.0056530.4In this paper, we experimentally verify the phenomenon of chaotic synchronization in coupled forced oscillators. The study is focused on the model of three double pendula locally connected via springs. Each of the individual oscillators can behave both periodically and chaotically, which depends on the parameters of the external excitation (the shaker). We investigate the relation between the strength of coupling between the upper pendulum bobs and the precision of their synchronization, showing that the system can achieve practical synchronization, within which the nodes preserve their chaotic character. We determine the influence of the pendula parameters and the strength of coupling on the synchronization precision, measuring the differences between the nodes' motion. The results obtained experimentally are confirmed by numerical simulations. We indicate a possible mechanism causing the desynchronization of the system's smaller elements (lower pendula bobs), which involves their motion around the unstable stationary position and possible transient dynamics. The results presented in this paper may be generalized into typical models of pendula and pendula-like coupled systems, exhibiting chaotic dynamics.

Amplification through chaotic synchronization in spatially extended beam-plasma systems.

In this paper, we have studied the relationship between chaotic synchronization and microwave signal amplification in coupled beam-plasma systems. We have considered a 1D particle-in-cell numerical model of unidirectionally coupled beam-plasma oscillatory media being in the regime of electron pattern formation. We have shown the significant gain of microwave oscillation power in coupled beam-plasma media being in the different regimes of generation. The discovered effect has a close connection with the chaotic synchronization phenomenon, so we have observed that amplification appears after the onset of the complete time scale synchronization regime in the analyzed coupled spatially extended systems. We have also provided the numerical study of physical processes in the chain of beam-plasma systems leading to the chaotic synchronization and the amplification of microwave oscillations power, respectively.

Image encryption process based on chaotic synchronization phenomena

This paper presents a novel image encryption scheme, which uses a chaotic True Random Bits Generator (TRBG). The chaotic TRBG is based on the coexistence of two different synchronization phenomena. The first one is the well-known complete chaotic synchronization while the second one is a recently new proposed synchronization phenomenon, the inverse π-lag synchronization. This coexistence is observed in the case of two mutually coupled identical nonlinear circuits. The nonlinear circuit, which is used, produces double-scroll chaotic attractors. The initial conditions of the coupled system and the values of the circuit's parameters serve as the private key of the proposed cryptographic scheme. In order to face the challenge of using this chaotic TRBG in such cryptographic schemes, the produced bits sequence is subjected to statistical tests which are the well-known Federal Information Processing Standards-140-2. This bits sequence has then been used to encrypt and decrypt gray-scale images. Also, the security analysis of the encrypted image demonstrates the high security of the proposed encryption scheme.

Chaotic synchronization of two complex nonlinear oscillators

Synchronization is an important phenomenon commonly observed in nature. It is also often artificially induced because it is desirable for a variety of applications in physics, applied sciences and engineering. In a recent paper [Mahmoud GM, Mohamed AA, Aly SA. Strange attractors and chaos control in periodically forced complex Duffing’s oscillators. Physica A 2001;292:193–206], a system of periodically forced complex Duffing’s oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. Their connection to solutions of the nonlinear Schrödinger equation has also been pointed out. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using active control and global synchronization techniques. We derive analytical expressions for control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Spatiotemporal Chaos Synchronization in Beam–Plasma Systems with Supercritical Current

It is established that coupled beam-plasma systems with supercritical current can feature the phenomenon of chaotic synchronization. As the coupling between subsystems increases, a distributed beam-plasma system exhibits the transition from asynchronous behavior via phase synchronization to the state of complete chaotic synchronization. The phenomenon of chaotic synchronization is studied using a method developed previously on the basis of the introduction of a continuous manifold of phases of the chaotic signal.

Estimating the Parameters of Semiconductor Optical-Feedback Lasers from Time Series

A new method is proposed for estimating the control parameters of single-mode semiconductor optical-feedback lasers from experimentally measured time series of the laser intensity. The procedure is based on a statistical analysis of specially selected points of the time series and on the phenomenon of chaotic synchronization of unidirectionally coupled lasers with coinciding parameters.

Chaotic Synchronization in a Five-Star-Coupled Phase-Locked Loop System

This paper describes a chaotic synchronization phenomenon observed experimentally in a five-star-coupled phase-locked loop (PLL) oscillator system. This system consists of five PLLs connected in the shape of a star. The state in this system itinerates between the completely synchronized state, in which all PLL oscillators synchronize, and the disordered state, in which all PLLs oscillate individually, via the partially synchronized state. The time-series of the voltage difference between arbitrary two PLL oscillators shows the on-off intermittency. When such a chaotic itinerancy occurs, the distribution function of the duration time of the completely synchronized state is expressed as a \(-\frac{3}{2}\) power law which is quite similar to the distribution function of the laminar duration time in the on-off intermittency.

Chaos synchronization and chaos anticontrol of a suspended track with moving loads

In this paper, we first study the chaotic synchronization phenomenon of the suspended track with moving load system and then the transient response of chaos synchronization. The Lyapunov exponent is utilized to prove the chaos synchronization, but under certain conditions it is more complicated. Next, we study the synchronization of autonomous and non-autonomous systems. We find that slave systems cannot be synchronized with master system for certain time excitations no matter how large A is. Next, the phase synchronization between them will be studied. An application of chaos synchronization and secure communication is presented. Finally, in order to increase the chaos phenomena, we use anticontrol. Constant torque, periodic torque, periodic impulse signal, time delay function, and adaptive control are used successfully to control the state from order to chaos.

CHAOTIC SYNCHRONIZATION: INFORMATION VIEWPOINT

The phenomenon of chaotic synchronization is investigated from an information viewpoint. The synchronization of a "receiver" of chaos with a chaotic "source" is discussed as an ability of the receiver to recover a copy of the chaotic signal generated by the source. The main idea of the paper is to show that in terms of the information approach the condition for the chaotic synchronization is not due to the physical effect of one system on the other, but the transmission of necessary information about the chaotic process and, hence, the information carrying capacity of the "communication channel" between the source and the receiver.

Chaotic synchronization as an information process

The chaotic synchronization phenomenon is studied from the information point of view. Synchronization of a chaos receiver by a chaos source is considered as copy recovery of the chaotic signal transmitted by the source. The main idea of this paper is to show that the necessary condition of chaotic synchronization is not the level of physical action of one system on another but the transmission of a certain volume of information on the chaotic process and, therefore, the capacity of the “communication channel” between the source and the receiver.

Chaotic synchronization in Hamiltonian systems.

It is shown that Hamiltonian systems can exhibit the phenomenon of chaotic synchronization. Specific attention is paid to the standard map. Analytic synchronization conditions are derived and numerically verified for the standard map. We report on experimental studies of an analog electronic circuit realization of a "piecewise linear standard map." When coupled appropriately to a duplicate circuit, chaotic synchronization is observed. The relevance of this study to synchronization in other Hamiltonian systems is discussed.