Oscillation death in systems of oscillators with transferable coupling and time-delay
Ming He - Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai, 200030, China (email)
Abstract: This paper addresses the oscillation death in systems of coupled neural oscillators. The coupling is assumed to be transferable and such transferable structure includes the nearest-neighbor coupling and the multiple-neighbor coupling. The death solution is obtained as a limit of upper solutions and lower solutions. We investigate a coupled cyclic chain of oscillators, in which the coupling is transferred in one direction and with a time lag. To obtain the asymptotic stability of the death solution, we establish the necessary and sufficient conditions to ensure the zeros for a class of exponential polynomials to lie to the left of the imaginary axis.
Keywords: Neural oscillator, oscillation death, transferability, time delay, stability,
Received: September 2000; Revised: May 2001; Published: July 2001.
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