Existence and Exponential Stability of Multiple Periodic Solutions for a Multidirectional Associative Memory Neural Network

Authors:
Tiejun Zhou;Min Wang;Min Long
Affiliations:
College of Science, Hunan Agricultural University, Changsha, China 410128 and College of Orient Science and Technology, Hunan Agricultural University, Changsha, China 410128;College of Orient Science and Technology, Hunan Agricultural University, Changsha, China 410128;College of Science, Hunan Agricultural University, Changsha, China 410128
Venue:
Neural Processing Letters
Year:
2012

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Abstract

The paper proposes several mathematical models of the multidirectional associative memory (MAM) neural network by analyzing its structure. A model of MAM with distributed delays is studied. Under some new assumptions on activation functions, $${2^{n_0[m/2]}}$$ invariant subsets of MAM are constructed. Then the existence and the exponential stability of $${2^{n_0[m/2]}}$$ periodic solutions located on invariant subsets are obtained by constructing a suitable Liapunov function and a Poincaré mapping. An estimating method of the exponential convergence rate is given. The obtained results are new to MAM neural networks. An example is given to illustrate the effectiveness of the results.