Abstract
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.
Highlights
Synchronization[1, 2] and suppression of oscillations[3,4,5,6] are two most prominent emergent dynamics of the coupled oscillators
There has been a lot of interest in understanding the transition from amplitude death (AD) to oscillation death (OD) in coupled oscillators and it has been found that a Hopf bifurcation in the coupled system stabilizes the trivial fixed point first, which on larger coupling gives birth to coupling dependent steady states known as homogeneous steady states (HSS) and inhomogeneous steady states (IHSS) through a pitchfork bifurcation[5, 6, 17]
We have studied the suppression of oscillations from oscillatory state of an ensemble of limit–cycle and chaotic oscillators from phase transition point of view
Summary
To describe this explosive transition, we first consider N identical Van der Pol (VdP) oscillators coupled via a mean–field diffusion. The dynamics of this coupled system can be written as, x i = yi + k(Qx − xi), y i = b(1 − xi2)yi − xi,. Where, i ( = 1, 2, ..., N ) is the index of the oscillators. B( > 0) indicates the non–linearity and strength of damping the of a VdP intensity oscillator.
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