Designing Coupling for Synchronization and Amplification of Chaos

Abstract

We propose a design of coupling for stable synchronization and antisynchronization in chaotic systems under parameter mismatch. The antisynchronization is independent of the specific symmetry (reflection symmetry, axial symmetry, or other) of a dynamical system. In the synchronization regimes, we achieve amplification (attenuation) of a chaotic driver in a response oscillator. Numerical examples of a Lorenz system, Rössler oscillator, and Sprott system are presented. Experimental evidence is shown using an electronic version of the Sprott system.

Design and FPGA implementation of a wireless hyperchaotic communication system for secure real-time image transmission

“…Precisely, since chaos is sensitive to small variations of its initial conditions and parameters, it is very difficult to synchronize two chaotic systems in a communication scheme. Some proposed synchronization techniques have improved the robustness to parameter mismatches as reported in [16,17], where impulsive chaotic synchronization and an open-loop-closed-loopbased coupling scheme are proposed, respectively. Other authors proposed to improve the robustness of chaotic synchronization to channel noise [18], where a coupled lattice instead of coupled single maps is used to decrease the master-slave synchronization error.…”

Inverse synchronization of coupled fractional-order systems through open-plus-closed-loop control

“…Further, the IS scheme is theoretically proved through the stability theorem of linear FDEs. The results reported in this paper have further extended the application of OPCL control in synchronizing integer-order and fractional-order systems [54][55][56][57][58][59][60]. Finally, we point out that although we consider only the coupled identical fractional-order systems, in many real world systems such as biological systems and laser arrays, it is hardly the case that every component can be assumed to be identical.…”

“…The OPCL control has found its applications in the synchronization of both integer-order and fractional-order differential systems [54][55][56][57][58][59][60]. Here, we shall further investigate its new applications in IS of the fractional-order differential systems.…”

Synchronization of indirectly coupled Lorenz oscillators: An experimental study

“…Different synchronization regimes have been observed between two unidirectional or bidirectional coupled chaotic Rössler circuit [24], Chua's circuits [25], van der Pol oscillator, Duffing oscillator [26] and Sprott circuits [27]. Synchronization and phase-flip in delay coupled Chua's circuit [28] and in-phase or anti-phase synchronization by open-loop-closed-loop (OPCL) based coupling in coupled electronic circuits is also observed [29].…”