The study of amplitude death in globally delay-coupled nonidentical systems based on order parameter expansion

The method of order parameter expansion is used to study the dynamical behavior in the globally delay-coupled nonidentical systems. Using the Landau-Stuart periodic system and Rossler chaotic oscillator to construct representative systems, the method can identify the boundary curves of amplitude death island analytically in the parameter space of the coupling and time delay. Furthermore, the parameter mismatch (diversity) effect on the size of island is investigated numerically. For the case of coupled chaotic Rossler systems with different timescales, the diversity increases the domain of death island monotonically. However, for the case of delay-coupled Landua-Stuart periodic systems with different frequencies, the average frequency turns out to be a critical role that determines change of size with the increase of diversity. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4730749]