Extreme stability and almost periodicity in continuous and discrete neuronal models with finite delays

ANZIAM J. 44 (2002), 261-282

Extreme stability and almost periodicity in continuous and discrete neuronal models with finite delays

S. Mohamad
On leave from Department of Mathematics
University Brunei Darussalam
Bandar Seri Begawan BE 1410
Brunei Darussalam
sannay@ubd.edu.bn
Current address:
Mathematics and Statistics
School of Informatics and Engineering
Flinders University of South Australia
Bedford Park SA 5042
Australia

and

K. Gopalsamy
Mathematics and Statistics
School of Informatics and Engineering
Flinders University of South Australia
Bedford Park SA 5042
Australia
gopal@ist.flinders.edu.au

Abstract

We consider the dynamical characteristics of a continuous-time isolated Hopfield-type neuron subjected to an almost periodic external stimulus. The model neuron is assumed to be dissipative having finite time delays in the process of encoding the external input stimulus and recalling the encoded pattern associated with the external stimulus. By using non-autonomous Halanay-type inequalities we obtain sufficient conditions for the hetero-associative stable encoding of temporally non-uniform stimuli. A brief study of a discrete-time model derived from the continuous-time system is given. It is shown that the discrete-time model preserves the stability conditions of the continuous-time system.

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