Explosive death in complex network.

We report the emergence of an explosive death transition in a network of identical oscillators interacting to other oscillators through nonlocal coupling in the presence of a common environment. This transition has an abrupt and irreversible characteristic in parameter space which has been a common signature of first order phase transition. For the similar coupling scheme, both ensemble of chaotic and periodic oscillators showed qualitatively similar kind of transition, hence making it a universal transition. The details of which along with dependence of environmental and nonlocal coupling on this first-order like phase transition is also discussed.

Explosive death induced by mean-field diffusion in identical oscillators.

We report the occurrence of an explosive death transition for the first time in an ensemble of identical limit cycle and chaotic oscillators coupled via mean-field diffusion. In both systems, the variation of the normalized amplitude with the coupling strength exhibits an abrupt and irreversible transition to death state from an oscillatory state and this first order phase transition to death state is independent of the size of the system. This transition is quite general and has been found in all the coupled systems where in-phase oscillations co-exist with a coupling dependent homogeneous steady state. The backward transition point for this phase transition has been calculated using linear stability analysis which is in complete agreement with the numerics.

Intermittent feedback induces attractor selection.

We present a method for attractor selection in multistable dynamical systems. It involves a feedback term that is active only when the dynamics of the system is in a particular fraction of state space of the attractor. We implement this method first on a simplest symmetric chaotic flow and then on a bistable neuronal system. We find that adding this space-dependent feedback term to the dynamical equations of these systems will drive the dynamics to the desired attractor by annihilating the other. We further demonstrate that the attractor selection due to this feedback term can be used in construction of logic gates, which is one of the practical applications of the proposed method.

Oscillation suppression in indirectly coupled limit cycle oscillators.

We study the phenomena of oscillation quenching in a system of limit cycle oscillators which are coupled indirectly via a dynamic environment. The dynamics of the environment is assumed to decay exponentially with some decay parameter. We show that for appropriate coupling strength, the decay parameter of the environment plays a crucial role in the emergent dynamics such as amplitude death (AD) and oscillation death (OD). The critical curves for the regions of oscillation quenching as a function of coupling strength and decay parameter of the environment are obtained analytically using linear stability analysis and are found to be consistent with the numerics.