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

Pages: 737 - 745, Volume 7, Issue 4, October 2001

doi:10.3934/dcds.2001.7.737       Abstract        Full Text (148.1K)       Related Articles

Ming He - Department of Applied Mathematics, Shanghai Jiao Tong University, Shanghai, 200030, China (email)
Xiaoyun Ma - Mathematics/Computer Science Department, University of San Diego, San Diego, CA 92110, United States (email)
Weijiang Zhang - 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, exponential polynomial.
Mathematics Subject Classification:  92C20, 34.

Received: September 2000;      Revised: May 2001;      Published: July 2001.