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The Lyapunov-Krasovskii functional method is the most commonly used method in the investigation of the stability of delayed systems.
Many interesting results on stochastic effects to the stability of delayed neural networks have been reported (see [16 23]).
Since [26], it is more important and necessary to investigate the stability of delayed NNs including leakage effects.
Up to now, many results on the stability of delayed neural networks have been developed [3 5].
Thus it is important for us to consider the delay effect on the stability of delayed neural networks.
To study the stability of delayed reaction-diffusion neural networks, for instance, see [24 31], and references therein.
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Thus it will be better to analyze the stability of delay differentia systems by using the representation of the solutions directly.
The stability of delay ordinary differential and difference equations and delay partial differential and difference equations with bounded operators acting on delay terms has been studied extensively in a large cycle of works (see [1 13] and the references therein) and insight has developed over the last three decades.
In order to answer this question, we first introduce the alternate delayed system, then we study the exponential stability of delayed chaotic neural networks by means of alternate control.
Huang [41] considered the exponential stability of delayed neural networks, but he also did not consider the effect of proportional delays and leakage delays.
And the asymptotic stability of delayed stochastic GRNs with impulsive effect was discussed in [19].
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