Stability in asymmetric Hopfield nets with transmission delays

K. Gopalsamy; Xue zhong He

doi:10.1016/0167-2789(94)90043-4

Stability in asymmetric Hopfield nets with transmission delays

K. Gopalsamy^*, Xue zhong He

^*Corresponding author for this work

Flinders University

Research output: Contribution to journal › Article › peer-review

535 Citations (Scopus)

Abstract

Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield's graded response networks of the type dx_i(t)/dt = -b_ix_i(t) + Σⁿ_{j = 1} a_ijf_j(μ_jx_j(t - τ_ij)) +F_i(t) (i = 1, 2, ..., n) when the external inputs F_i are held temporally uniform. A generalization to continuously distributed delays is briefly indicated. Several illustrative examples are numerically simulated and the results of simulations are graphically displayed.

Original language	English
Pages (from-to)	344-358
Number of pages	15
Journal	Physica D: Nonlinear Phenomena
Volume	76
Issue number	4
DOIs	https://doi.org/10.1016/0167-2789(94)90043-4
Publication status	Published - 15 Sept 1994
Externally published	Yes

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title = "Stability in asymmetric Hopfield nets with transmission delays",

abstract = "Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield's graded response networks of the type dxi(t)/dt = -bixi(t) + Σnj = 1 aijfj(μjxj(t - τij)) +Fi(t) (i = 1, 2, ..., n) when the external inputs Fi are held temporally uniform. A generalization to continuously distributed delays is briefly indicated. Several illustrative examples are numerically simulated and the results of simulations are graphically displayed.",

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AU - Gopalsamy, K.

AU - He, Xue zhong

PY - 1994/9/15

Y1 - 1994/9/15

N2 - Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield's graded response networks of the type dxi(t)/dt = -bixi(t) + Σnj = 1 aijfj(μjxj(t - τij)) +Fi(t) (i = 1, 2, ..., n) when the external inputs Fi are held temporally uniform. A generalization to continuously distributed delays is briefly indicated. Several illustrative examples are numerically simulated and the results of simulations are graphically displayed.

AB - Sufficient conditions are derived for the delay independent stability of the equilibria in Hopfield's graded response networks of the type dxi(t)/dt = -bixi(t) + Σnj = 1 aijfj(μjxj(t - τij)) +Fi(t) (i = 1, 2, ..., n) when the external inputs Fi are held temporally uniform. A generalization to continuously distributed delays is briefly indicated. Several illustrative examples are numerically simulated and the results of simulations are graphically displayed.

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U2 - 10.1016/0167-2789(94)90043-4

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AN - SCOPUS:0001075269

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SP - 344

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JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 4

ER -

Stability in asymmetric Hopfield nets with transmission delays

Abstract

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