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Global asymptotic stability analysis of bidirectional associative memory neural networks with distributed delays and impulse. (English) Zbl 1154.34380

The authors study existence and global asymptotic stability of the equilibrium point for the following system with distributed delays and impulses
\[ \frac{du_i(t)}{dt}=-a_iu_i(t)+\sum_{j=1}^m w_{ji}f_i\left(\int_0^{\infty}K_{ji}(s)v_j(t-s)ds\right)+c_i, t\not=t_k, \]
\[ \Delta u_i(t_k)=I_{ik}(u_i(t_k)), k=1,2,\dots, \]
\[ \frac{dv_j(t)}{dt}=-b_jv_j(t)+\sum_{i=1}^n v_{ij}g_i\left(\int_0^{\infty}N_{ij}(s)u_i(t-s)ds\right)+d_j, t\not=t_k, \]
\[ \Delta v_j(t_k)=J_{jk}(v_j(t_k)), k=1,2,\dots,\quad i=1,2,\dots,n;\quad j=1,2,\dots,m \]
To this end they construct a positive definite Lyapunov function.

MSC:

34K20 Stability theory of functional-differential equations
34K45 Functional-differential equations with impulses
92B20 Neural networks for/in biological studies, artificial life and related topics
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References:

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