Numerical simulation of periodic solutions for a class of numerical discretization neural networks

Mathematical and Computer Modelling

Volumn 52, Issue 1-2, 2010, Pages 386-396

  Lu, Chun ^a   Ding, Xiaohua ^b   Liu, Mingzhu ^b  

^a QINGDAO TECHNOLOGICAL UNIVERSITY   (China)

^b HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Coincidence degree; Globally exponentially stable; Lyapunov function; Neural network; Periodic solution

Indexed keywords

COINCIDENCE DEGREE; COINCIDENCE DEGREE THEORY; GLOBAL EXPONENTIAL STABILITY; GLOBALLY EXPONENTIALLY STABLE; NUMERICAL DISCRETIZATION; NUMERICAL SIMULATION; PERIODIC SOLUTION; SUFFICIENT CONDITIONS;

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; EXPONENTIAL FUNCTIONS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; PROBLEM SOLVING; TIME VARYING NETWORKS;

NEURAL NETWORKS;

EID: 77953133714     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.03.005     Document Type: Article

References (17)

1. Li Y.Q., and Huang L.H. Exponential convergence behavior of solutions to shunting inhibitory cellular neural networks with delays and time-varying coefficients. Math. Comput. Modelling 48 (2008) 499-504
2. Wu W., Cui B.T., and Lou X.Y. Global exponential stability of Cohen-Grossberg neural networks with distributed delays. Math. Comput. Modelling (2008) 868-873
3. Jiang H.J., and Cao J.D. BAM-type Cohen-Grossberg neural networks with time delays. Math. Comput. Modelling 47 (2008) 92-103
4. Guo S.J., and Huang L.H. Stability of nonlinear waves in a ring of neurons with delays. J. Differential Equations 236 (2007) 343-374
5. Liu Y.R., Wang Z.D., and Liu X.H. Asymptotic stability for neural networks with mixed time-delays: the discrete-time case. Neural Netw. 22 (2009) 67-74
6. Zhong S.M., and Liu X.Z. Exponential stability and periodicity of cellular neural networks with time delay. Math. Comput. Modelling 45 (2007) 1231-1240
7. Park J.H. A new stability analysis of delayed cellular neural networks. Appl. Math. Comput. 181 (2006) 200-205
8. Fan M., and Zou X.F. Global asymptotic stability of a class of nonautonomous integro-differential systems and applications. Nonlinear Anal. 57 (2004) 111-135
9. Mohamad S., and Naim A.G. Discrete-time analogues of integrodifferential equations modelling bidirectional neural networks. J. Comput. Appl. Math. 138 (2002) 1-20
10. Li Y.K. Global stability and existence of periodic solutions of discrete delayed cellular neural networks. Phys. Lett. A 333 (2004) 51-61
11. Mohamad S., and Gopalsamy K. Neuronal dynamics in time varying environments: continuous and discrete time models. Discrete Contin. Dyn. Syst. 6 (2000) 841-860
12. Liu P., and Cui X. A discrete model of competition. Math. Comput. Simulation 49 (1999) 1-12
13. Gaines R.E., and Mawhin J.L. Coincidence Degree and Nonlinear Differential Equations (1977), Springer-Verlag, Berlin
14. Yoshizawa T. Stability theory by Liapunov's second method (1966), Math. Soc. Japan, Tokyo
15. Yoshizawa T. Stability Theory and the Existence of Periodic Solutions and Almost-Periodic Solutions. Applied Math. Sciences vol. 14 (1975), Springer-Verlag
16. Fan M., and Wang K. Periodic solutions of a discrete time nonautonomous ratio-dependent predator-prey system. Math. Comput. Modelling 35 (2002) 951-961
17. Fan M., and Wang K. Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments. Math. Biosci. 160 (1999) 47-61