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

Published online by Cambridge University Press:  17 February 2009

S. Mohamad  and
K. Gopalsamy
S. Mohamad
Affiliation:
On leave from Department of Mathematics, University Brunei Darussalam, Bandar Serf Begawan BE, 1410, Brunei Darussalam; e-mail: sannay@ubd.edu.bn.
K. Gopalsamy
Affiliation:
Mathematics and Statistics, School of Informatics and Engineering, Flinders University of South Australia, Bedford Park SA 5042, Australia; e-mail: gopal@ist.flinders.edu.au.
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Abstract

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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.

Type
Research Article
Information
The ANZIAM Journal , Volume 44 , Issue 2 , October 2002 , pp. 261 - 282
Copyright
Copyright © Australian Mathematical Society 2002

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