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Research Papers

Global Stability and Bifurcation in Delayed Bidirectional Associative Memory Neural Networks With an Arbitrary Number of Neurons

[+] Author and Article Information
Elham Javidmanesh

Department of Applied Mathematics,
Ferdowsi University of Mashhad,
Mashhad 9177948974, Iran
e-mails: javidmanesh@ferdowsi.um.ac.ir; e_javidmanesh@yahoo.com

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received October 6, 2015; final manuscript received February 11, 2017; published online June 5, 2017. Assoc. Editor: Azim Eskandarian.

J. Dyn. Sys., Meas., Control 139(8), 081018 (Jun 05, 2017) (5 pages) Paper No: DS-15-1489; doi: 10.1115/1.4036229 History: Received October 06, 2015; Revised February 11, 2017

In this paper, delayed bidirectional associative memory (BAM) neural networks, which consist of one neuron in the X-layer and other neurons in the Y-layer, will be studied. Hopf bifurcation analysis of these systems will be discussed by proposing a general method. In fact, a general n-neuron BAM neural network model is considered, and the associated characteristic equation is studied by classification according to n. Here, n can be chosen arbitrarily. Moreover, we find an appropriate Lyapunov function that under a hypothesis, results in global stability. Numerical examples are also presented.

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References

Kosko, B. , 1987, “ Adaptive Bidirectional Associative Memories,” Appl. Opt. 26(23), pp. 4947–4960. [CrossRef] [PubMed]
Cao, J. , and Xiao, M. , 2007, “ Stability and Hopf Bifurcation in a Simplified BAM Neural Network With Two Time Delays,” IEEE Trans. Neural Networks 18(2), pp. 416–430. [CrossRef]
Ge, J. , and Xu, J. , 2011, “ Synchronization and Synchronized Periodic Solution in a Simplified Five-Neuron BAM Neural Network With Delays,” Neurocomputing, 74(6), pp. 993–999. [CrossRef]
Xu, C. , He, X. , and Li, P. , 2011, “ Global Existence of Periodic Solutions in a Six-Neuron BAM Neural Network Model With Discrete Delays,” Neurocomputing, 74(17), pp. 3257–3267. [CrossRef]
Xu, C. , Tang, X. , and Liao, M. , 2010, “ Frequency Domain Analysis for Bifurcation in a Simplified Tri-Neuron BAM Network Model With Two Delays,” Neural Networks, 23(7), pp. 872–880. [CrossRef] [PubMed]
Yang, Y. , and Ye, J. , 2009, “ Stability and Bifurcation in a Simplified Five-Neuron BAM Neural Network With Delays,” Chaos Solitons Fractals, 42(4), pp. 2357–2363. [CrossRef]
Zhang, T. , Jiang, H. , and Teng, Z. , 2009, “ On the Distribution of the Roots of a Fifth Degree Exponential Polynomial With Application to a Delayed Neural Network Model,” Neurocomputing, 72(4–6), pp. 1098–1104. [CrossRef]
Javidmanesh, E. , Afsharnezhad, Z. , and Effati, S. , 2013, “ Existence and Stability Analysis of Bifurcating Periodic Solutions in a Delayed Five-Neuron BAM Neural Network Model,” Nonlinear Dyn., 72(1), pp. 149–164. [CrossRef]
Perko, L. , 2001, Differential Equations and Dynamical Systems, Springer, Berlin.
Haddad, W. M. , and Chellaboina, V. , 2008, Nonlinear Dynamical Systems and Control: A Lyapunov-Based Approach, Princeton University Press, Oxford, UK.

Figures

Grahic Jump Location
Fig. 1

A family of periodic solutions bifurcate from the origin and Hopf bifurcation occurs

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