Amplitude death in oscillators coupled by a one-way ring time-delay connection.
The coupling induced stabilization of a steady state, which is called amplitude death, cannot be observed in identical nonlinear oscillators coupled by diffusive connections. However, it has been analytically confirmed that amplitude death can be induced by using a diffusive time-delay coupling. In this paper, a one-way ring time-delay coupled system consisting of N identical oscillators is proposed. This system is equivalent to a delayed-feedback control system when N=1, and to a time-delay coupled oscillator system when N=2. In the proposed system, amplitude death never occurs at a steady state when the Jacobi matrix evaluated at a fixed point has an odd number of real positive eigenvalues. Furthermore, a simple systematic graphical procedure to test the stability of the system is presented. This procedure is illustrated in two numerical examples: coupled Rössler oscillators and coupled Lorenz oscillators.
Konishi
Keiji
K
Department of Complex Systems, Future University-Hakodate, 116-2 Kamedanakano, Hakodate, Hokkaido 041-8655, Japan. kkonishi@fun.ac.jp