Intermittency transition to generalized synchronization in coupled time-delay systems

Abstract

In this paper, we report the nature of transition to generalized synchronization (GS) in a system of two coupled scalar piecewise linear time-delay systems using the auxiliary system approach. We demonstrate that the transition to GS occurs via on-off intermittency route and also it exhibits characteristically distinct behaviors for different coupling configurations. In particular, the intermittency transition occurs in a rather broad range of coupling strength for error feedback coupling configuration and in a narrow range of coupling strength for direct feedback coupling configuration. It is also shown that the intermittent dynamics displays periodic bursts of period equal to the delay time of the response system in the former case, while they occur in random time intervals of finite duration in the latter case. The robustness of these transitions with system parameters and delay times has also been studied for both linear and nonlinear coupling configurations. The results are corroborated analytically by suitable stability conditions for asymptotically stable synchronized states and numerically by the probability of synchronization and by the transition of subLyapunov exponents of the coupled time-delay systems. We have also indicated the reason behind these distinct transitions by referring to unstable periodic orbit theory of intermittency synchronization in low-dimensional systems.

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

“…Synchronizing such time-delay systems is very challenging and has potential applications in diverse areas involving physical, chemical, biological, neurological and electrical systems [13][14][15][16][17]. Different types of synchronization have been recently observed numerically along with experimental evidence in coupled time-delay systems [18][19][20][21][22].…”

A unified framework of exponential synchronization for complex networks with time-varying delays

“…This means that they fail to conclude whether the complex networks can be synchronized or not. Turning to the method proposed in this Letter for help, however, we find the conditions in Theorems 1 and 2 are satisfied which implies that we obtain a more effective method than that of [24][25][26]. On the other hand, the methods suggested in [27][28][29] are concerned with discrete-time networks.…”

“…It should be pointed out that [24][25][26] can only deal with constant time delay. Ever in such a case (we assume μ = 0 for Examples 1-3), it is verified that there is no feasible solution for the results of [24][25][26]. This means that they fail to conclude whether the complex networks can be synchronized or not.…”

“…This problem was further studied by Senthilkumar et al [25]. The intermittency transition to generalized synchronization form a desynchronized state in unidirectional coupled scalar piecewise linear time-delay systems for different coupling configurations using the auxiliary system approach was addressed in [26]. However, the time delays in their model are constant and the obtained results are independent of time delay.…”

Design of coupling for synchronization in time-delayed systems

“…In a GS state the response system develop a functional relationship with the driver. GS in delay systems without coupling delay [35,36] and with delay coupling [37] was also investigated, however, the coupling is assumed a priori known. Instead, we design the delay coupling for engineering a GS state [23] or closely delay systems.…”