Exponential stability of inertial BAM neural network with time-varying impulses and mixed time-varying delays via matrix measure approach

Abstract This article is concerned with the effects of time-varying impulses on exponential stability to a unique equilibrium point of inertial Bidirectional Associative Memories (BAM) neural network with mixed time-varying delays. A suitable variable transformation is chosen to transform the original system into a system of first order differential equations. The concept of homeomorphism has been implemented to find a distributed delay-dependent sufficient condition which assures that the system has a unique equilibrium point. In order to study the impulsive effects on stability problems, a time-varying impulses, including stabilizing and destabilizing impulses, are considered with the transformed system. Based on the matrix measure approach and an extended impulsive differential inequality for a time-varying delayed system, we have derived sufficient criteria in matrix measure form which ensure the exponential stability of the system towards an equilibrium point for two classes of activation functions. Further, different convergence rates of the system’s trajectory have been discussed for the cases of time-varying stabilizing and destabilizing impulses using the concept of an average impulsive interval. Finally, the efficiency of the theoretical results has been illustrated by providing two numerical examples.

[1]  Yong Li,et al.  Matrix measure strategies for stabilization and synchronization of delayed BAM neural networks , 2016 .

[2]  Qiankun Song,et al.  LMI criteria on exponential stability of BAM neural networks with both time-varying delays and general activation functions , 2010, Math. Comput. Simul..

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

[4]  Huaguang Zhang,et al.  A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[5]  B Kosko,et al.  Adaptive bidirectional associative memories. , 1987, Applied optics.

[6]  Jigui Jian,et al.  Global convergence analysis of impulsive inertial neural networks with time-varying delays , 2017, Neurocomputing.

[7]  Martin Bohner,et al.  An impulsive delay differential inequality and applications , 2012, Comput. Math. Appl..

[8]  Yunquan Ke,et al.  Stability analysis of BAM neural networks with inertial term and time delay , 2011 .

[9]  Wei Zhang,et al.  Robust Stability of Inertial BAM Neural Networks with Time Delays and Uncertainties via Impulsive Effect , 2018, Neural Processing Letters.

[10]  Huamin Wang,et al.  Distributed-delay-dependent exponential stability of impulsive neural networks with inertial term , 2018, Neurocomputing.

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

[12]  Jigui Jian,et al.  Global exponential convergence for impulsive inertial complex-valued neural networks with time-varying delays , 2019, Math. Comput. Simul..

[13]  Yang Tang,et al.  Stability of delayed neural networks with time-varying impulses , 2012, Neural Networks.

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

[15]  Wei Zhang,et al.  Stability of inertial delayed neural networks with impulsive effect , 2017, 2017 International Workshop on Complex Systems and Networks (IWCSN).

[16]  Jigui Jian,et al.  Exponential synchronization of inertial neural networks with mixed time-varying delays via periodically intermittent control , 2019, Neurocomputing.

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

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

[19]  A. Tesi,et al.  New conditions for global stability of neural networks with application to linear and quadratic programming problems , 1995 .

[20]  Frank L. Lewis,et al.  Multistability of Delayed Hybrid Impulsive Neural Networks With Application to Associative Memories , 2019, IEEE Transactions on Neural Networks and Learning Systems.

[21]  Robert M. Westervelt,et al.  Stability and dynamics of simple electronic neural networks with added inertia , 1986 .

[22]  Chuandong Li,et al.  Stability of inertial BAM neural network with time-varying delay via impulsive control , 2015, Neurocomputing.

[23]  Yuliya N. Kyrychko,et al.  Dynamics of Neural Systems with Discrete and Distributed Time Delays , 2015, SIAM J. Appl. Dyn. Syst..

[24]  K. Gopalsamy,et al.  Exponential stability of continuous-time and discrete-time cellular neural networks with delays , 2003, Appl. Math. Comput..

[25]  Weirui Zhao,et al.  Global exponential stability analysis of Cohen–Grossberg neural network with delays , 2008 .

[26]  Gail A. Carpenter,et al.  Neural network models for pattern recognition and associative memory , 1989, Neural Networks.

[27]  Chuandong Li,et al.  Bogdanov-Takens bifurcation in a single inertial neuron model with delay , 2012, Neurocomputing.

[28]  Jinde Cao,et al.  Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays , 2014, Neural Networks.

[29]  Jigui Jian,et al.  Matrix measure based exponential stabilization for complex-valued inertial neural networks with time-varying delays using impulsive control , 2018, Neurocomputing.

[30]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[31]  BART KOSKO,et al.  Bidirectional associative memories , 1988, IEEE Trans. Syst. Man Cybern..

[32]  Jingfeng Wang,et al.  Global Lagrange stability for inertial neural networks with mixed time-varying delays , 2017, Neurocomputing.

[33]  Alireza Nazemi.  A dynamic system model for solving convex nonlinear optimization problems , 2012 .