Global attracting sets for neutral-type BAM neural networks with time-varying and infinite distributed delays

Abstract In this paper, the asymptotic property of a class of neutral-type BAM neural networks with time-varying and infinite distributed delays is discussed. By developing a new integral inequality and applying the properties of nonnegative matrix, some sufficient conditions for the Lagrange stability and the existence of the global attracting set of the considering model are obtained. Meanwhile, the estimation of the global attractive set is also given out. The results derived here generalize and improve the earlier publications. Finally, two numerical examples are given and analyzed to demonstrate our results.

[1]  J. P. Lasalle.  The stability of dynamical systems , 1976 .

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

[3]  Jinde Cao,et al.  Exponential stability and periodic oscillatory solution in BAM networks with delays , 2002, IEEE Trans. Neural Networks.

[4]  Jigui Jian,et al.  New estimations for ultimate boundary and synchronization control for a disk dynamo system , 2013 .

[5]  Qiankun Song,et al.  Stability analysis of fuzzy cellular neural networks with time delay in the leakage term and impulsive perturbations , 2012, J. Frankl. Inst..

[6]  Delay‐dependent asymptotic stability of BAM neural networks with time delay , 2010 .

[7]  Jinde Cao,et al.  New results on the existence and uniqueness of almost periodic solution for BAM neural networks with continuously distributed delays , 2007 .

[8]  Hongyong Zhao.  Global stability of bidirectional associative memory neural networks with distributed delays , 2002 .

[9]  Jigui Jian,et al.  Stability in Lagrange sense for Cohen–Grossberg neural networks with time-varying delays and finite distributed delays , 2010 .

[10]  Hongyong Zhao.  Invariant set and attractor of nonautonomous functional differential systems , 2003 .

[11]  Jinde Cao,et al.  Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms , 2005 .

[12]  Jinde Cao,et al.  Global exponential stability of bidirectional associative memory neural networks with distributed delays , 2007 .

[13]  Xiaodi Li,et al.  Exponential stability for stochastic reaction-diffusion BAM neural networks with time-varying and distributed delays , 2011, Appl. Math. Comput..

[14]  Ahmad Haidar,et al.  Delay-range-dependent control synthesis for time-delay systems with actuator saturation , 2008, Autom..

[15]  Jinde Cao,et al.  Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays , 2003 .

[16]  Dao-Yi Xu,et al.  Integro-differential equations and delay integral inequalities , 1992 .

[17]  Daoyi Xu,et al.  Global attracting set for non-autonomous neutral type neural networks with distributed delays , 2012, Neurocomputing.

[18]  Zhigang Zeng,et al.  Positive invariant and global exponential attractive sets of neural networks with time-varying delays , 2008, Neurocomputing.

[19]  Wei Zhu.  Global exponential stability of impulsive reaction-diffusion equation with variable delays , 2008, Appl. Math. Comput..

[20]  Daoyi Xu,et al.  Attracting and invariant sets for a class of impulsive functional differential equations , 2007 .

[21]  Rajendran Samidurai,et al.  New delay dependent robust asymptotic stability for uncertain stochastic recurrent neural networks with multiple time varying delays , 2012, J. Frankl. Inst..

[22]  Zhengwen Tu,et al.  Global dissipativity of a class of BAM neural networks with time-varying and unbound delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[23]  Bart Kosko,et al.  Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence , 1991 .

[24]  B. R. Upadhyaya,et al.  Performance analysis and application of the bidirectional associative memory to industrial spectral signatures , 1989, International 1989 Joint Conference on Neural Networks.

[25]  Daoyi Xu,et al.  Exponential stability of nonlinear impulsive neutral differential equations with delays , 2007 .

[26]  Li Yu,et al.  Exponential stability analysis for neutral BAM neural networks with time-varying delays and stochastic disturbances , 2012 .

[27]  Hongjiong Tian.  The exponential asymptotic stability of singularly perturbed delay differential equations with a bounded lag , 2002 .

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

[29]  Qiming Liu,et al.  Periodic Solutions of Cohen-Grossberg-Type BAM Neural Networks with Time-Varying Delays , 2012 .