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... 3 (see [38]). Given any real matrix...

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... dynamic performance [3–5]. Hence, it is significant and necessary to take into account the delay effects on dynamics of neural networks, for example, existence, uniqueness and stability, and so on. To date, neural network models with two categories of time delays, namely, discrete and continuously distributed time delays, have been extensively investigated by many researchers, using some effective approaches; see [6– 22] and references therein. For instance, in [6], Kharitonov and Zhabko studied the robust stability of time-delay systems via Lyapunov-Krasovskii functional approach. Wu et al. [9] introduced free-weighting matrix approach and investigated the robust stability problem for time-varying delay systems. Gu introduced the delay decomposition method in [10]. Recently, a special type of time delay, namely, leakage delay (or forgetting delay), is identified and investigated due to its existence in many real systems. In 2007, Gopalsamy [11] proposed the bidirectional associative memory neural networks with constant delay in the leakage term and derived sufficient conditions for existence and stability of equilibrium. Based on this work, Li and Huang [12] investigated the stabili...

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...ngineer, and neural networks [1–5]. Moreover, time delays can affect the stability of a neural network and create oscillatory and bad dynamic performance [3–5]. Hence, it is significant and necessary to take into account the delay effects on dynamics of neural networks, for example, existence, uniqueness and stability, and so on. To date, neural network models with two categories of time delays, namely, discrete and continuously distributed time delays, have been extensively investigated by many researchers, using some effective approaches; see [6– 22] and references therein. For instance, in [6], Kharitonov and Zhabko studied the robust stability of time-delay systems via Lyapunov-Krasovskii functional approach. Wu et al. [9] introduced free-weighting matrix approach and investigated the robust stability problem for time-varying delay systems. Gu introduced the delay decomposition method in [10]. Recently, a special type of time delay, namely, leakage delay (or forgetting delay), is identified and investigated due to its existence in many real systems. In 2007, Gopalsamy [11] proposed the bidirectional associative memory neural networks with constant delay in the leakage term and der...

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... and stability, and so on. To date, neural network models with two categories of time delays, namely, discrete and continuously distributed time delays, have been extensively investigated by many researchers, using some effective approaches; see [6– 22] and references therein. For instance, in [6], Kharitonov and Zhabko studied the robust stability of time-delay systems via Lyapunov-Krasovskii functional approach. Wu et al. [9] introduced free-weighting matrix approach and investigated the robust stability problem for time-varying delay systems. Gu introduced the delay decomposition method in [10]. Recently, a special type of time delay, namely, leakage delay (or forgetting delay), is identified and investigated due to its existence in many real systems. In 2007, Gopalsamy [11] proposed the bidirectional associative memory neural networks with constant delay in the leakage term and derived sufficient conditions for existence and stability of equilibrium. Based on this work, Li and Huang [12] investigated the stability of general nonlinear systems with leakage delay, bymodel transformation, contractionmapping theorem, and degenerate Lyapunov-Krasovskii functional. However, dynamical ana...

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...ted by many researchers, using some effective approaches; see [6– 22] and references therein. For instance, in [6], Kharitonov and Zhabko studied the robust stability of time-delay systems via Lyapunov-Krasovskii functional approach. Wu et al. [9] introduced free-weighting matrix approach and investigated the robust stability problem for time-varying delay systems. Gu introduced the delay decomposition method in [10]. Recently, a special type of time delay, namely, leakage delay (or forgetting delay), is identified and investigated due to its existence in many real systems. In 2007, Gopalsamy [11] proposed the bidirectional associative memory neural networks with constant delay in the leakage term and derived sufficient conditions for existence and stability of equilibrium. Based on this work, Li and Huang [12] investigated the stability of general nonlinear systems with leakage delay, bymodel transformation, contractionmapping theorem, and degenerate Lyapunov-Krasovskii functional. However, dynamical analysis of neural networks with time delay in leakage term has been little considered due to some theoretical and technical difficulties [23–30]. In fact, time delay in the stabilizing n...

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...ther sudden noises; that is, it does exhibit impulsive Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2014, Article ID 327070, 14 pages http://dx.doi.org/10.1155/2014/327070 2 Abstract and Applied Analysis effects; see [13–21, 31–35]. Therefore, impulsive perturbations should be taken into account when studying the dynamics of neural networks. Since the existence of delays and impulses is frequently a source of instability, bifurcation, and chaos for dynamical systems, it is significant to study both delay and impulsive effects on dynamical systems [13–21, 25, 26, 32]. In [25], Li et al. investigated the existence, uniqueness, and stability problems of recurrent neural networks with discrete time delay and time delay in the leakage termunder impulsive perturbations, while being without distributed delay. Since neural networks usually have a spatial extent, there is a distribution of propagation delays over a period of time. In these circumstances the signal propagation is not instantaneous and cannot be modelled only with discrete delays and a more appropriate way is to incorporate continuously distributed delays in neural network models. To the best of our knowled...

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...ional approach. Wu et al. [9] introduced free-weighting matrix approach and investigated the robust stability problem for time-varying delay systems. Gu introduced the delay decomposition method in [10]. Recently, a special type of time delay, namely, leakage delay (or forgetting delay), is identified and investigated due to its existence in many real systems. In 2007, Gopalsamy [11] proposed the bidirectional associative memory neural networks with constant delay in the leakage term and derived sufficient conditions for existence and stability of equilibrium. Based on this work, Li and Huang [12] investigated the stability of general nonlinear systems with leakage delay, bymodel transformation, contractionmapping theorem, and degenerate Lyapunov-Krasovskii functional. However, dynamical analysis of neural networks with time delay in leakage term has been little considered due to some theoretical and technical difficulties [23–30]. In fact, time delay in the stabilizing negative feedback term has a tendency to destabilize a system [11] and has great impact on the dynamics of neural networks. On the other hand, besides delay, impulses are also likely to exist in neural networks. In impl...

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...rbations, while being without distributed delay. Since neural networks usually have a spatial extent, there is a distribution of propagation delays over a period of time. In these circumstances the signal propagation is not instantaneous and cannot be modelled only with discrete delays and a more appropriate way is to incorporate continuously distributed delays in neural network models. To the best of our knowledge, so far, there has been very little existing work on impulsive neural networks with time delay in the leakage term and discrete and time-varying distributed delays via LMI approach [27]. Motivated by aforementioned discussion, in this paper, we consider a class of impulsive neural networks with mixed timedelays and generalized activation functionswhich could be different from each other. The mixed time delays include time-varying transmission delay, bounded timevarying distributed delay, and constant delay in the leakage term. Firstly, by using the contraction mapping theorem, we obtain a delay-independent sufficient condition to guarantee the global existence and uniqueness of the solution for the addressed neural networks. Secondly, we present a delayindependent sufficient...

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