Effective synchronization of a class of Chua's chaotic systems using an exponential feedback coupling

In this work a robust exponential function based controller is designed to synchronize effectively a given class of Chua's chaotic systems. The stability of the drive-response systems framework is proved through the Lyapunov stability theory. Computer simulations are given to illustrate and verify the method.Comment: 12 pages, 18 figure

Finite-time synchronization of tunnel diode based chaotic oscillators

This paper addresses the problem of finite-time synchronization of tunnel diode based chaotic oscillators. After a brief investigation of its chaotic dynamics, we propose an active adaptive feedback coupling which accomplishes the synchronization of tunnel diode based chaotic systems with and without the presence of delay(s), basing ourselves on Lyapunov and on Krasovskii-Lyapunov stability theories. This feedback coupling could be applied to many other chaotic systems. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at a pre-established time. An advantage of the proposed feedback coupling is that it is simple and easy to implement. Both mathematical investigations and numerical simulatioComment: 11 pages, 43 figure

A Simple and Robust Gray Image Encryption Scheme Using Chaotic Logistic Map and Artificial Neural Network

A robust gray image encryption scheme using chaotic logistic map and artificial neural network (ANN) is introduced. In the proposed method, an external secret key is used to derive the initial conditions for the logistic chaotic maps which are employed to generate weights and biases matrices of the multilayer perceptron (MLP). During the learning process with the backpropagation algorithm, ANN determines the weight matrix of the connections. The plain image is divided into four subimages which are used for the first diffusion stage. The subimages obtained previously are divided into the square subimage blocks. In the next stage, different initial conditions are employed to generate a key stream which will be used for permutation and diffusion of the subimage blocks. Some security analyses such as entropy analysis, statistical analysis, and key sensitivity analysis are given to demonstrate the key space of the proposed algorithm which is large enough to make brute force attacks infeasible. Computing validation using experimental data with several gray images has been carried out with detailed numerical analysis, in order to validate the high security of the proposed encryption scheme

Complex behaviors in a new 4D memristive hyperchaotic system without equilibrium and its microcontroller-based implementation

The construction of dynamic systems with new features has always been an interesting research topic. Since the introduction of the first memristor model, several memristive systems have been reported. This paper focuses on a new memristive hyperchaotic system without equilibrium, emerging from the extended diffusionless Lorenz equations. Its rich dynamics is demonstrated by using familiar tools. Hyperchaos, very long transient chaotic regimes, rare bursting oscillations schemes and coexistence of four attractors are noticed. A low-cost microcontroller-based implementation for digital engineering applications is presented to confirm its feasibility

Infinitely Many Coexisting Attractors in No-Equilibrium Chaotic System

This paper proposes a new no-equilibrium chaotic system that has the ability to yield infinitely many coexisting hidden attractors. Dynamic behaviors of the system with respect to the parameters and initial conditions are numerically studied. It shows that the system has chaotic, quasiperiodic, and periodic motions for different parameters and coexists with a large number of hidden attractors for different initial conditions. The circuit and microcontroller implementations of the system are given for illustrating its physical meaning. Also, the synchronization conditions of the system are established based on the adaptive control method

Network of mobile systems: mutual influence of oscillators and agents

This work presents a network of mobile systems whose nodes are constituted by a moving agent with an internal state (an oscillator), which influences each other. The coupling topology of the agents and internal oscillators changes over time according to the interaction range (also called vision range or vision sizes (Majhi et al. Phys Rev E 99: 012308, 2019)) of their corresponding counterparts. The goal is to investigate the dynamics of the oscillators and the agents in the considered systems. Our results show that the synchronization between agents and that between oscillators depends on the coupling parameter of the oscillators, the velocity of the agents and the interaction range of both agents and oscillators. We have found that the vision range of the oscillators has a great influence on the dynamics of the agents. Among this dynamics, we can mention phase synchronization and clusters formation in the mobile system and complete synchronization as well as clusters formation on the oscillators. The stability of the synchronization in the oscillators is investigated using the Master Stability Function (MSF) developed by Pecora and Carroll (Phys Rev Lett 80: 2109, 1998)

Mobile oscillators network with amplification

In this work, we investigate the dynamics of a multilayer network of mobile agents with amplification where each agent is composed of two parts: internal dynamics defined by a Rössler chaotic oscillator and external dynamics defined by the random motion of this agent in 2D space. Each agent characterized by a communication range named ‘vision range’ which is the greatest distance within which two agents can exchange information and therefore establish a coupling. Thus, two cases were studied: the case where only the external dynamic influences the internal dynamic and the case where there is a mutual influence of the internal dynamic on the external dynamic and vice versa. The study of the effects of these parameters leads the internal dynamics of the network to the synchronization (resp. attenuation) and the spatial motion of the agent to the phase synchronization