Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays

A single inertial BAM neural network with time-varying delays and external inputs is concerned in this paper. First, by choosing suitable variable substitution, the original system can be transformed into first-order differential equations. Then, we present several sufficient conditions for the global exponential stability of the equilibrium by using matrix measure and Halanay inequality, these criteria are simple in form and easy to verify in practice. Furthermore, when employing an error-feedback control term to the response neural network, parallel criteria regarding to the exponential synchronization of the drive-response neural network are also generated. Finally, some examples are given to illustrate our theoretical results.

[1]  K. Gopalsamy,et al.  Time delays and stimulus-dependent pattern formation in periodic environments in isolated neurons , 2002, IEEE Trans. Neural Networks.

[2]  S. Ruan,et al.  Stability and bifurcation in a neural network model with two delays , 1999 .

[3]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .

[4]  Kwok-Wo Wong,et al.  Hopf Bifurcation on a Two-Neuron System with Distributed Delays: A Frequency Domain Approach , 2003 .

[5]  Zhao Hong-yong,et al.  Bifurcation and control of a class of inertial neuron networks , 2011 .

[6]  Jun Tani,et al.  Model-based learning for mobile robot navigation from the dynamical systems perspective , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[7]  Christof Koch,et al.  Cable theory in neurons with active, linearized membranes , 2004, Biological Cybernetics.

[8]  W. Singer,et al.  Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties , 1989, Nature.

[9]  邓飞其,et al.  “Time Delays and Stimulus-Dependent Pattern Formation in Periodic Environments in Isolated Neurons’’的注记 , 2005 .

[10]  Jinde Cao,et al.  Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays , 2004, Neural Networks.

[11]  Jun Tani.  Proposal of chaotic steepest descent method for neural networks and analysis of their dynamics , 1992 .

[12]  X. Liao,et al.  Stability of bifurcating periodic solutions for a single delayed inertial neuron model under periodic excitation , 2009 .

[14]  Dora E. Angelaki,et al.  Models of membrane resonance in pigeon semicircular canal type II hair cells , 1991, Biological Cybernetics.

[15]  B. D. Coleman,et al.  Periodic Solutions of Certain Nonlinear Integral Equations with a Time Lag , 1976 .

[16]  Diek W. Wheeler,et al.  Stability and chaos in an inertial two-neuron system , 1997 .

[17]  Bimal K. Bose,et al.  Expert system, fuzzy logic, and neural network applications in power electronics and motion control , 1994, Proc. IEEE.

[18]  Colin H. Hansen,et al.  Stability and dynamics of a controlled van der Pol-Duffing oscillator , 2006 .

[19]  Ke Yunquan,et al.  Stability and existence of periodic solutions in inertial BAM neural networks with time delay , 2013, Neural Computing and Applications.

[20]  Jinde Cao,et al.  Estimation on Domain of Attraction and Convergence Rate of Hopfield Continuous Feedback Neural Networks , 2001, J. Comput. Syst. Sci..

[21]  B. H. Blott,et al.  Review of neural network applications in medical imaging and signal processing , 1992, Medical and Biological Engineering and Computing.

[22]  X. Liao,et al.  Hopf bifurcation and chaos in a single inertial neuron model with time delay , 2004, nlin/0411027.

[23]  D. Attwell,et al.  Models for electrical tuning in hair cells , 1985, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[24]  Wischert,et al.  Delay-induced instabilities in nonlinear feedback systems. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[25]  Xiaofeng Liao,et al.  The Research for Hopf Bifurcation in a Single Inertial Neuron Model with External Forcing , 2007 .

[26]  Jinde Cao,et al.  Exponential synchronization of chaotic neural networks: a matrix measure approach , 2009 .

[27]  Feng Yang,et al.  Improved Algorithm of BP Neural Network and its Application to Prediction of K/S Value in Dyeing with Reactive Dyes , 2007 .

[28]  X. Liao,et al.  Bifurcation analysis on a two-neuron system with distributed delays , 2001 .

[29]  Xiaofeng Liao,et al.  Stability switches and bifurcation analysis of a neural network with continuously delay , 1999, IEEE Trans. Syst. Man Cybern. Part A.

[30]  Wai Keung Wong,et al.  Distributed Synchronization of Coupled Neural Networks via Randomly Occurring Control , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[31]  Jinde Cao,et al.  Boundedness and stability for Cohen–Grossberg neural network with time-varying delays☆ , 2004 .

[32]  Yunquan Ke,et al.  Stability analysis of inertial Cohen-Grossberg-type neural networks with time delays , 2013, Neurocomputing.

[33]  Takeo Kanade,et al.  Neural Network-Based Face Detection , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[34]  X. Liao,et al.  Dynamics of an inertial two-neuron system with time delay , 2009 .