Resmi V, Ambika G, Amritkar RE. General mechanism for amplitude death in coupled systems.
PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011;
84:046212. [PMID:
22181250 DOI:
10.1103/physreve.84.046212]
[Citation(s) in RCA: 53] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2011] [Revised: 09/05/2011] [Indexed: 05/31/2023]
Abstract
We introduce a general mechanism for amplitude death in coupled synchronizable dynamical systems. It is known that when two systems are coupled directly, they can synchronize under suitable conditions. When an indirect feedback coupling through an environment or an external system is introduced in them, it is found to induce a tendency for antisynchronization. We show that, for sufficient strengths, these two competing effects can lead to amplitude death. We provide a general stability analysis that gives the threshold values for onset of amplitude death. We study in detail the nature of the transition to death in several specific cases and find that the transitions can be of two types--continuous and discontinuous. By choosing a variety of dynamics, for example, periodic, chaotic, hyperchaotic, and time-delay systems, we illustrate that this mechanism is quite general and works for different types of direct coupling, such as diffusive, replacement, and synaptic couplings, and for different damped dynamics of the environment.
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