Inverse anticipating chaos synchronization

Abstract

We report a new type of chaos synchronization:inverse anticipating synchronization, where a time delay chaotic system x can drive another system y in such a way that the driven system anticipates the driver by synchronizing with its inverse future state:y(t) = −x(t + τ ),τ > 0. We extend the concept of inverse anticipating chaos synchronization to cascaded systems. We propose means for the experimental observation of inverse anticipating chaos synchronization in external cavity lasers. PACS number (s) . Application of chaos synchronization can be found in secure communications, optimization of non-linear systems' performance, modeling brain activity and pattern recognition [2]. Synchronization of coupled chaotic systems restricts the evolution of synchronized systems to the synchronization manifold and therefore eliminates some degrees of freedom of the joint system, and thus leading to significant reduction of complexity. In this context new types of chaos synchronization can be considered as a novel ways of reducing unpredictability of chaotic dynamics. Time delay systems are ubiquitous in nature, technology and society due to finite signal transmission times, switching speeds and memory effects [3]. Therefore the study of chaos synchronization in these systems is of high practical importance. Because of their ability to generate high-dimensional chaos time delay systems are also good candidates for secure communications based on chaos synchronization [4]. In addition, time delay systems can be considered as a special case of spatio-temporal systems [5].In this letter we report a new type of synchronization: inverse anticipating synchronization, where a time-delayed chaotic system x drives another system y in such a way that the driven system anticipates the driver by synchronizing with its inverse future state:x(t) = −y(t − τ ) (in conditional representation:x = −y τ ) or equivalently y(t) = −x(t + τ ) with τ > 0. We investigate inverse anticipating synchronization between two coupled systems both with a single delay time and with two characteristic delay times where the delay time in the coupling is different from the delay time in the coupled systems themselves. We extend our findings to cascaded systems. We also propose means for the experimental observation of inverse anticipating synchronization phenomenon using external cavity laser diodes. We define inverse anticipating synchronization as follows: the driver system

Complete synchronization of the noise-perturbed Chua’s circuits

“…19 could be further generalized to investigate the complete synchronization of other oscillators, such as the Lorenz-type systems, 29,30 the BAM neural network models 31 and the complex networks, and even some other types of synchronization, such as generalized synchronization due to parameter mismatches. 32 However, it should be mentioned that when one is to make these generalizations, an extended invariance principle for stochastic differential equations should be developed. This is because, take the Lorenz-type systems, for example, the nonlinear term in the systems does not satisfy the globally Lipschitz condition, so that the boundedness of the sampling path generated by the noise-perturbed systems cannot be guaranteed.…”

Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

“…The Ikeda model was introduced to describe the dynamics of an optical bistable resonator, plays an important role in electronics and physiological studies and is well-known for delay-induced chaotic behavior [14,15,8,16]. Physically x is the phase lag of the electric field across the resonator; a is the relaxation coefficient for the driving x and driven y dynamical variables; m 1,2 and m 3,4 are the laser intensities injected into the driving and driven systems, respectively.…”

“…Recently in [8] we reported a type of synchronization: inverse anticipating synchronization, where a time-delayed chaotic system x drives another system y in such a way that a driven system anticipates the driver by synchronizing to its inverse future state: x(t) = Ày s Ày(t À s) or equivalently y(t) = Àx(t + s) with s > 0. (We notice that the phenomenon of inverse synchronization is generic.…”

“…The authors of [9] prefer to use the term ''anti-synchronization'' for the phenomenon.) In paper [8], we focused our attention on cases when a driving system contain a single delay time.…”

Slave–master dynamics of semiconductor laser with short external cavity

“…Systems of DDEs now occupy a place of central importance in all areas of science, such as neural networks [13] and biological systems [14]. In many earlier works, output intensity (or field amplitude) fluctuations and their synchronization have been the main themes in considering chaos synchronization in lasers [15][16][17][18]. However, it should be noted that the chaotic light injected from ML into the SL will fluctuate chaotically in the optical output intensity of the SL.…”