Oscillation death in systems of oscillators with transferable coupling and time-delay

Ming He; Xiaoyun Ma; Weijiang Zhang

doi:10.3934/dcds.2001.7.737

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2001, Volume 7, Issue 4: 737-745. Doi: 10.3934/dcds.2001.7.737

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Oscillation death in systems of oscillators with transferable coupling and time-delay

1.
Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai, 200030
2.
Mathematics/Computer Science Department, University of San Diego, San Diego, CA 92110

Received: August 31, 2000

Revised: April 30, 2001

Published: September 2001

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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.

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Mathematics Subject Classification: 92C20, 34.

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