Amplitude death induced by dynamic coupling

Abstract

The present paper shows that dynamic coupling induces amplitude death in coupled identical oscillators. For a simple limit-cycle oscillator, our theoretical analysis provides the necessary and sufficient condition for amplitude death. Furthermore, we guarantee that amplitude death never occurs, if each oscillator satisfies the odd number property that is known in the field of delayed-feedback control of chaos.

Amplitude death: The emergence of stationarity in coupled nonlinear systems

“…Konishi [14] has proposed another type of interaction which, in contrast to the cases discussed above has an evolving or "dynamic" coupling. Consider the Landau-Stuart systeṁ [14].ẏ…”

“…Konishi and coworkers [14,37,73,74] have studied a number of models with different types of connections, on networks of varying topologies. Analytical estimation of regimes of amplitude death have been carried out, and their analysis shows that the odd-number property that is known in delayed feedback control also exits in global dynamically coupled oscillators.…”

“…Different situations where amplitude death occurs have been described, and it is now known that the phenomenon can be seen when the interacting systems are identical [7,11,12,13], mismatched [1,6], when the coupling is dynamical [14], or nonlinear (nondiffusive) [15]. We review these various situations and also discuss the general mechanism for AD in Sec.…”

Amplitude Death Induced by a Global Dynamic Coupling

“…It was recently reported that amplitude death in two coupled identical oscillators can be induced by incorporating a dynamic coupling without a time delay [Konishi, 2003b;Konishi, 2004b]. These reports provided the following results: the death was observed in both numerical simulations and electronic circuit experiments [Konishi, 2003b;Konishi, 2004b]; a sufficient condition under which death never occurs was derived [Konishi, 2003b]; and a necessary and sufficient condition for death in van der Pol oscillators was obtained [Konishi, 2004b].…”

Untitled

“…After then several works have been reported showing such transition in different coupled system like; mean field diffusive (MFD) coupled system [14], [15], time-delayed system [16], dynamic coupled system [17], conjugate coupled system [18], [19], diffusive and repulsive coupled system [20], [21] etc.…”