Neuronal dynamics in time varying enviroments: Continuous and discrete time models

S. Mohamad; K. Gopalsamy

doi:10.3934/dcds.2000.6.841

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2000, Volume 6, Issue 4: 841-860. Doi: 10.3934/dcds.2000.6.841

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Neuronal dynamics in time varying enviroments: Continuous and discrete time models

S. Mohamad^1, and
K. Gopalsamy^1,

1.
School of Informatics and Engineering, Flinders University of South Australia, Bedford Park SA 5042

Received: April 30, 1999

Revised: April 30, 2000

Published: September 2000

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Abstract

The convergence characteristics of an isolated Hopfield-type neuron in time varying environments are considered in particular when the neuronal parameters are assumed to be almost periodic. This study includes the investigations of neurons having periodic parameters but the periods are not integrally dependent. Both continuous-time-continuous-state and discrete-time-continuous-state models are discussed. Sufficient conditions are established for associative stimulus. It is shown that when the nreronal gain is dominated by the neuronal dissipation on average, associative recall of the encoded temporal pattern is guaranteed and this is achieved by the global stability of the encoded pattern.

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Mathematics Subject Classification: 34C27, 34D23, 39A12, 92B20, 65C20, 65D30.

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