Stability analysis of inertial Cohen-Grossberg-type neural networks with time delays

Abstract In this paper, the global exponential stability of inertial Cohen–Grossberg-type neural networks with time delays is investigated. First, by properly chosen variable substitution the system is transformed to the first order differential equation. Second, some sufficient conditions which can ensure the global exponential stability of the system are obtained using homeomorphism and differential mean value theorem, applying the analysis method and inequality technique. Finally, two examples are given to illustrate the effectiveness of the results.

[1]  X. Lou,et al.  Global asymptotic stability of BAM neural networks with distributed delays and reaction–diffusion terms , 2006 .

[2]  Jian Xu,et al.  Weak resonant Double Hopf bifurcations in an Inertial Four-Neuron Model with Time Delay , 2012, Int. J. Neural Syst..

[3]  Kelin Li,et al.  Exponential stability of impulsive Cohen-Grossberg neural networks with time-varying delays and reaction-diffusion terms , 2008, Neurocomputing.

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

[5]  Zuoan Li,et al.  Stability analysis of impulsive Cohen-Grossberg neural networks with distributed delays and reaction-diffusion terms , 2009 .

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

[7]  Tingwen Huang,et al.  Robust stability of delayed fuzzy Cohen-Grossberg neural networks , 2011, Comput. Math. Appl..

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

[9]  Chuandong Li,et al.  Stability of Cohen-Grossberg neural networks with unbounded distributed delays , 2007 .

[10]  Jinde Cao,et al.  Stability of Cohen-Grossberg neural networks with time-varying delays , 2007, Neural Networks.

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

[12]  Guoyin Wang,et al.  Research for Hopf bifurcation of an inertial two-neuron system with time delay , 2006, 2006 IEEE International Conference on Granular Computing.

[13]  Q. Song,et al.  Global exponential stability of impulsive Cohen-Grossberg neural network with time-varying delays , 2008 .

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

[15]  Qintao Gan,et al.  Exponential synchronization of stochastic Cohen-Grossberg neural networks with mixed time-varying delays and reaction-diffusion via periodically intermittent control , 2012, Neural Networks.

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

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

[19]  Zidong Wang,et al.  Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays , 2008 .

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

[21]  Qintao Gan,et al.  Adaptive synchronization of Cohen–Grossberg neural networks with unknown parameters and mixed time-varying delays , 2012 .

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

[23]  Shumin Fei,et al.  Stability analysis of Cohen-Grossberg neural networks with time-varying and distributed delays , 2008, Neurocomputing.

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

[25]  Y. Horikawa,et al.  Bifurcation and stabilization of oscillations in ring neural networks with inertia , 2009 .

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