American Institute of Mathematical Sciences

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October  2001, 7(4): 737-745. doi: 10.3934/dcds.2001.7.737

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

Ming He 1, , Xiaoyun Ma 2, and  Weijiang Zhang 1,

1. 

Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai, 200030, China, China
2. 

Mathematics/Computer Science Department, University of San Diego, San Diego, CA 92110, United States

Received  September 2000 Revised  May 2001 Published  July 2001

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, exponential polynomial., oscillation death, transferability, stability, time delay.
Mathematics Subject Classification: 92C20, 3.
Citation: Ming He, Xiaoyun Ma, Weijiang Zhang. Oscillation death in systems of oscillators with transferable coupling and time-delay. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 737-745. doi: 10.3934/dcds.2001.7.737
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