• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.211-225
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• 2011

In this paper, a class of bi-directional associative memory (BAM) fuzzy cellular neural networks with distributed delays and impulses is formulated and investigated. By employing an integro-differential inequality with impulsive initial conditions and the topological degree theory, some sufficient conditions ensuring the existence and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with distributed delays are obtained. In particular, the estimate of the exponential convergence rate is also provided, which depends on the delay kernel functions and system parameters. 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.

• Journal of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-240
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• 2011

In this paper, the problem on periodic solutions of the bidirectional associative memory neural networks with both periodic coefficients and periodic time-varying delays is discussed. By using degree theory, inequality technique and Lyapunov functional, we establish the existence, uniqueness, and global asymptotic stability of a periodic solution. The obtained results of stability are less restrictive than previously known criteria, and the hypotheses for the boundedness and monotonicity on the activation functions are removed.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.1031-1049
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• 2012

In this paper, a class of impulsive fuzzy bi-directional associative memory (BAM) neural networks with distributed delays and variable coefficients are considered. Using Lyapunov functional method and fixed point theorem, we derived some sufficient conditions for the existence and globally exponential stability of unique periodic solution of the networks. The results obtained are new and extend the previous known results. In addition, an example is given to show the effectiveness of our results obtained.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.727-747
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• 2011

By employing coincidence degree theory and using Halanay-type inequality technique, a sufficient condition is given to guarantee the existence and global exponential stability of periodic solutions for the two-dimensional discrete-time Cohen-Grossberg BAM neural networks. Compared with the results in existing papers, in our result on the existence of periodic solution, the boundedness conditions on the activation are replaced with global Lipschitz conditions. In our result on the existence and global exponential stability of periodic solution, the assumptions in existing papers that the value of activation functions at zero is zero are removed.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.279-292
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• 2011

In this paper, we consider anti-periodic solutions of the following BAM neural networks with multiple delays on time scales: $$\{{x^\Delta_i(t)=-a_i(t)e_i(x_i(t))+{\sum\limits^m_{j=1}}c_{ji}(t)f_j(y_j(t-{\tau}_{ji}))+I_i(t),\atop y^\Delta_j(t)=-b_j(t)h_j(y_j(t))+{\sum\limits^n_{i=1}}d_{ij}(t)g_i(x_i(t-{\delta}_{ij}))+J_j(t),}\$$ where i = 1, 2, ..., n,j = 1, 2, ..., m. Using some analysis skills and Lyapunov method, some sufficient conditions on the existence and exponential stability of the anti-periodic solution to the above system are established.

• Journal of applied mathematics & informatics
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• v.29 no.1_2
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• pp.103-117
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• 2011

By using an important lemma, some analysis techniques and Lyapunov functional method, we establish the sufficient conditions of the existence of equilibrium solution of a class of BAM neural network with impulses and distributed delays. Finally, applications and an example are given to illustrate the effectiveness of the main results.