Amplitude Death in Extended Time-Delay Coupled Oscillator Networks

Abstract

The present paper applies the concept of extended delayed feedback control, a commonly used method for controlling chaos, to a quenching phenomenon (i.e., amplitude death) in time-delay coupled oscillator networks. We show that a simple characteristic function governs the stability of amplitude death. The simple function enables us to explicitly obtain the stability ranges of the delay time. These ranges depend on the number of oscillators and the network topology. Thus, for situations where the number of oscillators and/or network topology are unknown, one cannot determine the delay time that induces amplitude death. We propose a simple procedure for designing a delay time for which amplitude death is locally stable for any number of oscillators and any network topology. The theoretical results are confirmed by numerical examples. In addition, it is found that the stability ranges of the delay time are much wider than those for conventional delay-coupled oscillator networks.

Keywords

• Amplitude death
• extended time-delay feedback
• oscillator networks
• stability analysis