Oscillatory behaviour is essential for proper functioning of various physical and biological processes. However, diffusive coupling is capable of suppressing intrinsic oscillations due to the manifestation of the phenomena of amplitude and oscillation deaths. Here we present a scheme to revoke these quenching states in diffusively coupled dynamical networks, and demonstrate the approach in experiments with an oscillatory chemical reaction. By introducing a simple feedback factor in the diffusive coupling, we show that the stable (in)homogeneous steady states can be effectively destabilized to restore dynamic behaviours of coupled systems. Even a feeble deviation from the normal diffusive coupling drastically shrinks the death regions in the parameter space. The generality of our method is corroborated in diverse non-linear systems of diffusively coupled paradigmatic models with various death scenarios. Our study provides a general framework to strengthen the robustness of dynamic activity in diffusively coupled dynamical networks.
Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article we report the first identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a new transformation of the attractors and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems. Synchronization is a natural phenomenon that one encounters in daily life. Since the identification of chaotic synchronization [1, 2, 3], several papers have appeared in identifying and demonstrating basic kinds of synchronization both theoretically and experimentally (cf. [4,5]). Among them, chaotic phase synchronization (CPS) refers to the coincidence of characteristic time scales of the coupled systems, while their amplitudes of oscillations remain chaotic and often uncorrelated. Phase synchronization (PS) plays a crucial role in understanding the behavior of a large class of weakly interacting dynamical systems in diverse natural systems. Examples include circadian rhythm, cardio-respiratory systems, neural oscillators, population dynamics, electrical circuits, etc [4,5,6].The notion of CPS has been investigated so far in oscillators driven by external periodic force [7,8], chaotic oscillators with different natural frequencies and/or with parameter mismatches [9,10,11,12], arrays of coupled chaotic oscillators [13,14] and also in essentially different chaotic systems [15,16]. On the other hand PS in nonlinear time-delay systems, which form an important class of dynamical systems, have not yet been identified and addressed. A main problem here is to define even the notion of phase in time-delay systems due to the intrinsic multiple characteristic time scales in these systems. Studying PS in such chaotic time-delay systems is of considerable importance in many fields, as in understanding the behavior of nerve cells (neuroscience), where memory effects play a prominent role, in pathological and physiological studies, in ecology, in lasers etc * Electronic address: lakshman@cnld.bdu.ac.in † Electronic address: jkurths@gmx.de [4,5,6,17,18,19,20,21]. In this paper, we report the first identification of phase synchronization (PS) in nonidentical time-delay systems in the hyperchaotic regime with non-phase coherent attractors with unidirectional nonlinear coupling. We will show the entrainment of phases of a coupled piecewise linear time-delay system for weak coupling from the non-synchronized state. Phase is calculated using the Poincaré method [4,5] after a new transformation of attractors of the time-delay systems, w...
By introducing a processing delay in the coupling, we find that it can effectively annihilate the quenching of oscillation, amplitude death (AD), in a network of coupled oscillators by switching the stability of AD. It revives the oscillation in the AD regime to retain sustained rhythmic functioning of the networks, which is in sharp contrast to the propagation delay with the tendency to induce AD. This processing delay-induced phenomenon occurs both with and without the propagation delay. Further this effect is rather general from two coupled to networks of oscillators in all known scenarios that can exhibit AD, and it has a wide range of applications where sustained oscillations should be retained for proper functioning of the systems.
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