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MiS Preprint

Total and partial amplitude death in networks of diffusively coupled oscillators

Fatihcan M. Atay


Networks of weakly nonlinear oscillators are considered with diffusive and time-delayed coupling. Averaging theory is used to determine parameter ranges for which the network experiences amplitude death, whereby oscillations are quenched and the equilibrium solution has a large domain of attraction. The amplitude death is shown to be a common phenomenon, which can be observed regardless of the precise nature of the nonlinearities and under very general coupling conditions. In addition, when the network consists of dissimilar oscillators, there exist parameter values for which only parts of the network are suppressed. Sufficient conditions are derived for total and partial amplitude death in arbitrary network topologies with general nonlinearities, coupling coefficients, and connection delays.

MSC Codes:
34C15, 34K, 92B20
02.30.Ks, 84.35.+i, 87.10.+e, 05.45.+b
coupled oscillators, time delay, stability, neural networks

Related publications

2003 Repository Open Access
Fatihcan M. Atay

Total and partial amplitude death in networks of diffusively coupled oscillators

In: Physica / D, 183 (2003) 1/2, pp. 1-18