Abstract
In the paper, a delay-differential equation modeling a bidirectional associative memory neural networks (BAM NNs) with reaction-diffusion terms is investigated, for which the input and output variables are varied with the time and space variables. By taking advantage of the inequality techniques, some Lyapunov-Krasovskii functional candidates are introduced to arrive at the novel sufficient conditions that warrant the passivity of spatially and temporally BAM NNs with mixed time delays. Moreover, when the parameter uncertainties appear in spatially and temporally BAM NNs, the criterion for robust passivity is also given. Novel passivity criteria are proposed in terms of inequalities, which can be checked easily. A numerical example is provided to demonstrate the effectiveness of the proposed results.
Highlights
Since NNs related to BAM had been proposed by Kosko [ ], the bidirectional associative memory neural networks (BAM NNs) have been one of the most interesting research and extensively studied topics due to their potential applications in pattern recognition, etc
Several sufficient general conditions are derived for the robust passivity of delayed BAM NNs with reaction-diffusion terms by using Lyapunov functional method and Poincaré integral inequality, which are very convenient to verify
6 Conclusions In this paper, we have investigated the passivity analysis problem for a class of spatially and temporally BAM NNs with mixed time delays
Summary
Since NNs related to BAM had been proposed by Kosko [ ], the BAM NNs have been one of the most interesting research and extensively studied topics due to their potential applications in pattern recognition, etc. The passivity theory was first proposed in the circuit analysis [ ], and since it has found successful applications in diverse areas such as stability [ , ], signal processing [ ], complexity [ ], fuzzy control [ ], and synchronization control [ ]. To the best of our knowledge, few authors considered the passivity problem for delayed RDNNs. It is interesting and important to discuss the passivity of RDNNs, in which the input and output variables are varied with the time and space variables. Several sufficient general conditions are derived for the robust passivity of delayed BAM NNs with reaction-diffusion terms by using Lyapunov functional method and Poincaré integral inequality, which are very convenient to verify. A numerical example is illustrated to show the usefulness of the proposed criteria
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