zbMATH — the first resource for mathematics

Mean square exponential stability and periodic solutions of stochastic delay cellular neural networks. (English) Zbl 1154.34395
Summary: This paper mainely concerns the exponential stability analysis and the existence of periodic solution problems for a class of stochastic cellular neural networks with discrete delays (SDCNNs). Above all, Poincare contraction theory is utilized to derive the conditions guaranteeing the existence of periodic solutions of SDCNNs. Next, Lyapunov function, stochastic analysis theory and Young inequality approach is developed to derive some theorems which gives several sufficient conditions such that periodic solutions of SDCNNs are mean square exponential stable. These sufficient conditions only including those governing parameters of SDCNNs can be easily checked by simple algebraic methods. Finally, two examples are given to demonstrate that the proposed criteria are useful and effective.

34K50 Stochastic functional-differential equations
34K13 Periodic solutions to functional-differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
Full Text: DOI
[1] Chua, L.O.; Yang, L., Cellular neural networks: theory, IEEE trans circ syst, 35, 10, 1257-1272, (1988) · Zbl 0663.94022
[2] Chua, L.O.; Yang, L., Cellular neural networks: applications, IEEE trans circ syst, 35, 10, 1273-1290, (1988)
[3] Roska, T.; Chua, L.O., Int J circ theory appl, 20, 469, (1992)
[4] Roska, T.; Wu, C.W.; Chua, L.O., Stability of cellular neural networks with dominant nonlinear and delay-type templates, IEEE trans circ syst pt I, 40, 4, 270, (1993) · Zbl 0800.92044
[5] Roska, T.; Wu, C.W.; Balsi, M., Stability dynamics of delay-type general cellular neural networks, IEEE trans circ syst pt I, 39, 6, 487, (1992) · Zbl 0775.92010
[6] Gilli, M., Stability of cellular neural networks and delayed cellular neural networks with nonpositive templates and nonmonotonic output functions, IEEE trans circ syst pt I, 41, 518-528, (1994)
[7] Cao, J., Stability analysis of delayed cellular neural networks, Neural networks, 11, 9, 1601, (1998)
[8] Arik, S., Equilibrium analysis of delayed cnns, IEEE trans circ syst pt I, 45, 2, 168-171, (1998)
[9] Cao, J., Phys rev E, 59, 5, 5940, (1999)
[10] Mastsuoka, K., Stability conditions for nonlinear continuous neural networks with asymmetric connection weights, Neural networks, 5, 495-500, (1992)
[11] Civalleri, P.P., On stability of cellular neural networks with delay, IEEE trans circ syst, 40, 3, 157, (1993) · Zbl 0792.68115
[12] Liao, X.X., Sci China ser A, 24, 10, 1037, (1994)
[13] Wang, Z., IEEE trans neural networks, 17, 814-820, (2006)
[14] Wan, L.; Sun, J., Mean square exponential stability of stochastic delayed Hopfield neural networks, Phys lett A, 343, 306-318, (2006) · Zbl 1194.37186
[15] Wang, Z., Robust stability for stochastic delay neural networks with time delays, Nonlin anal: real world appl, 7, 1119-1128, (2006) · Zbl 1122.34065
[16] Blythe, S.; Mao, X.; Liao, X., Stability of stochatic delay neural networks, J franklin inst, 338, 481-495, (2001) · Zbl 0991.93120
[17] Wang, Z., Exponential stability of uncertain stochastic neural networks with mixed time-delays, Chaos, solitions & fractals, 32, 62-72, (2007) · Zbl 1152.34058
[18] Liao, X.; Mao, X., Exponential stability and instability of stochastic neural networks, Stochast anal appl, 14, 2, 165-185, (1996) · Zbl 0848.60058
[19] Cao, Jinde, New results concerning exponential stability and periodic solutions of delayed cellular neural networks, Phys lett A, 307, 36C147, (2003) · Zbl 1006.68107
[20] Mao, X., Stochastic differential equations and application, (1997), Ellis Horwood · Zbl 0884.60052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.