Oscillation and global asymptotic stability of a neuronic equation with two delays

Hassan A. El-Morshedy, Abha Teachers' College, Abha, Saudi Arabia
B. M. El-Matary, Damietta Faculty of Science, New Damietta, Egypt

E. J. Qualitative Theory of Diff. Equ., No. 6. (2008), pp. 1-21.

Communicated by Bo Zhang. Received on 2007-05-09
Appeared on 2008-02-04

Abstract: In this paper we study the oscillatory and global asymptotic stability of a single neuron model with two delays and a general activation function. New sufficient conditions for the oscillation and nonoscillation of the model are given. We obtain both delay-dependent and delay-independent global asymptotic stability criteria. Some of our results are new even for models with one delay.

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