Abstract: In this paper, a class of impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms is formulated and investigated. By establishing a delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.
Abstract: In neural networks, when new patterns are learned by a network, the new information radically interferes with previously stored patterns. This drawback is called catastrophic forgetting or catastrophic interference. In this paper, we propose a biologically inspired neural network model which overcomes this problem. The proposed model consists of two distinct networks: one is a Hopfield type of chaotic associative memory and the other is a multilayer neural network. We consider that these networks correspond to the hippocampus and the neocortex of the brain, respectively. Information given is firstly stored in the hippocampal network with fast learning algorithm. Then the stored information is recalled by chaotic behavior of each neuron in the hippocampal network. Finally, it is consolidated in the neocortical network by using pseudopatterns. Computer simulation results show that the proposed model has much better ability to avoid catastrophic forgetting in comparison with conventional models.
Abstract: In this paper, a class of generalized bi-directional associative memory (BAM) neural networks with mixed delays is investigated. On the basis of Lyapunov stability theory and contraction mapping theorem, some new sufficient conditions are established for the existence and uniqueness and globally exponential stability of equilibrium, which generalize and improve the previously known results. One example is given to show the feasibility and effectiveness of our results.
Abstract: In this paper, a class of impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms is formulated and investigated. By employing the delay differential inequality and inequality technique developed by Xu et al., some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays and reaction-diffusion terms are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on system parameters, diffusion effect and impulsive disturbed intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.
Abstract: Hopfield model of associative memory is studied in this work. In particular, two main problems that it possesses: the apparition of spurious patterns in the learning phase, implying the well-known effect of storing the opposite pattern, and the problem of its reduced capacity, meaning that it is not possible to store a great amount of patterns without increasing the error probability in the retrieving phase. In this paper, a method to avoid spurious patterns is presented and studied, and an explanation of the previously mentioned effect is given. Another technique to increase the capacity of a network is proposed here, based on the idea of using several reference points when storing patterns. It is studied in depth, and an explicit formula for the capacity of the network with this technique is provided.
Abstract: In this paper, a novel associative memory model will be proposed and applied to memory retrievals based on the conventional continuous time model. The conventional model presents memory capacity is very low and retrieval process easily converges to an equilibrium state which is very different from the stored patterns. Genetic Algorithms is well-known with the capability of global optimal search escaping local optimum on progress to reach a global optimum. Based on the well-known idea of Genetic Algorithms, this work proposes a heuristic rule to make a mutation when the state of the network is trapped in a spurious memory. The proposal heuristic associative memory show the stored capacity does not depend on the number of stored patterns and the retrieval ability is up to ~ 1.
Abstract: This paper is concerned with the delay-distributiondependent
stability criteria for bidirectional associative memory
(BAM) neural networks with time-varying delays. Based on the
Lyapunov-Krasovskii functional and stochastic analysis approach,
a delay-probability-distribution-dependent sufficient condition is derived
to achieve the globally asymptotically mean square stable of
the considered BAM neural networks. The criteria are formulated in
terms of a set of linear matrix inequalities (LMIs), which can be
checked efficiently by use of some standard numerical packages. Finally,
a numerical example and its simulation is given to demonstrate
the usefulness and effectiveness of the proposed results.