A 4-dimensional nonlinear dynamical system is proposed for secure communications using chaos synchronization. It is shown that the chaotic attractor of the system has complex local structure that is sensitive to the perturbation of the system’s parameters. With the aid of the nonlinear forecasting technique, these properties have proven to be very useful in improving the security of communicati...

We study synchronization processes in networks of slightly nonidentical chaotic systems, for which a complete invariant synchronization manifold does not rigorously exist. We show and quantify how a slightly dispersed distribution in parameters can be properly modeled by a noise term affecting the stability of the synchronous invariant solution emerging for identical systems when the parameter ...

Chaos theory has a manifold variety of applications in science and engineering. There are many systems in nature with several stable states, which are separated by energy barriers. When the system can move along the stable states, its dynamics can become quite complex. A simple mechanical model that depicts some of these complex dynamical features is the famous Duffing double-well oscillator (1...

The aim of this communication is to study the chaos synchronization of coupled Sprott model L via hybrid feedback control method and tracking control method. Numerical simulation is performed to test the analytical findings.

For the first time, using a modified Ikeda model it is demonstrated analytically that anticipating synchronization can be obtained in chaotic time-delay systems governed by two characteristic delay times. We derive existence and stability conditions for the dual-time anticipating synchronization manifold. We also show that increased anticipation times for chaotic time-delay systems with two cha...

This investigation applies the adaptive fuzzy-neural observer (AFNO) to synchronize a class of unknown chaotic systems via scalar transmitting signal only. The proposed method can be used in synchronization if nonlinear chaotic systems can be transformed into the canonical form of Lur'e system type by the differential geometric method. In this approach, the adaptive fuzzy-neural network (FNN) i...

We report on the experimental observation of the generalized synchronization of chaos in a real physical system. We show that under a nonlinear resonant interaction, the chaotic dynamics of a single mode laser can become functionally related to that of a chaotic driving signal and furthermore as the coupling strength is further increased, the chaotic dynamics of the laser approaches that of the...

Referring to incommensurate and commensurate fractional systems, this article presents a new approach to investigate the coexistence of some synchronization types between non-identical systems characterized by different dimensions and different orders. In particular, the paper shows that complete synchronization (CS), anti-synchronization (AS) and inverse full state hybrid function projective s...

In this paper, we analyze chaotic dynamics of nonlinear systems and study chaos synchronization of Lorenz system. We extend our study by discussing other methods available in literature. We propose a theorem followed by a lemma in general and another one for a particular case of Lorenz system. Numerical simulations are given to verify the proposed theorems.

This paper studies basic dynamics from a novel pulse-coupled network (PCN). The unit element of the PCN is an integrate-and-fire circuit (IFC) that exhibits chaos. We an give an iff condition for the chaos generation. Using two IFC, we construct a master-slave PCN. It exhibits interesting chaos synchronous phenomena and their breakdown phenomena. We give basic classification of the phenomena an...