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

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  • 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.
    Mathematics Subject Classification: 92C20, 34.


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