Synchronization of Irregular Complex Networks with Chaotic Oscillators: Hamiltonian Systems Approach

Abstract

Synchronization of multiple chaotic oscillators in Hamiltonian form is numerically studied and is achieved by appealing to complex systems theory [1][2][3][4][5]. The topology that we consider is the irregular coupled network. Two cases are considered: i) chaotic synchronization without master oscillator (where the final collective behaviour is a new chaotic state) and ii) chaotic synchronization with master oscillator (where the final collective behaviour is imposed by the dynamics of the master oscillator to multiple slave oscillators). The Hysteretic and Rössler chaotic oscillators in Hamiltonian form will be used as examples.

FPGA realization of a chaotic communication system applied to image processing

“…This section reviews the multi-scroll chaotic oscillator based on saturated nonlinear function series that are approached by piece- wise linear (PWL) functions to be realized in an FPGA, as already shown in [2]. The mathematical model is given by (1), where a, b, c and d 1 are positive constants and the PWL function is denoted by f .…”

“…In particular, Hamiltonian forms have been developed to synchronize different kinds of chaotic topologies [1]. However, still very few works have been presented for either or both: realizing chaotic oscillators [2] and synchronization techniques [3], using field-programmable gate arrays (FPGAs).…”

“…In this article, we apply Hamiltonian forms [1] and observer approach to synchronize multi-scroll chaotic oscillators. The parameter values of the observers are approached analytically, like in [7], or in [8], where the synchronization is extended to multi-directional chaotic systems.…”

“…Section 3 summarizes the synchronization of two chaotic oscillators by Hamiltonian forms and observer approach [1]. Section 4 details the synchronization in a master-slave topology.…”

Analysis and Design of Adaptive Synchronization of a Complex Dynamical Network with Time-Delayed Nodes and Coupling Delays

“…In the past decade, special attention has been paid to the synchronization of dynamical systems, particularly largescale and complex networks of chaotic oscillators [15,16]. With the discovery of the small-world effect and scale-free feature of most complex networks, a lot of works have been concentrated on synchronization in small-world networks and scale-free networks [17][18][19][20].…”