Invariant set and attractivity of nonlinear differential equations with delays

Applied Mathematics Letters

Volumn 15, Issue 3, 2002, Pages 321-325

  Xu, Daoyi ^a   Zhao, Hongyong ^b  

^a SICHUAN UNIVERSITY   (China)

^b NANJING UNIVERSITY   (China)

Author keywords

Attracting set; Attraction basin; Delay differential equation; Nonlinear and nonautonomous

Indexed keywords

EID: 31244437438     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(01)00138-0     Document Type: Article

References (15)

1. K. Sawano, Positively invariant sets for functional differential equations with infinite delay, Tôhoku Math. J. 32 (2), 557-566, (1980).
2. G. Seifert, Positively invariant closed sets for systems of delay differential equations, J. Differential Equations 22, 292-304, (1976).
3. P. Bates, K. Lu and C. Zeng, Existence and persistence of invariant manifold for semiflows in Banach space, Memoirs of Amer. Math. Soc., 645, (1998).
4. D.D. Siljak, Large-Scale Dynamic System: Stability and Structure, Elsevier North-Holland, New York, (1978).
5. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Volume I, Academic Press, New York, (1969).
6. A.N. Michel, A.F. Jay and P. Wolfgand, Qualitative analysis of neural networks, IEEE Transactions on Circuits and Systems 36, 229-243, (1989).
7. A.V. Razgulin, The attractor of the delayed functional-differential diffusion equation. Numerical methods in mathematical physics, Comput. Math. Model 8, 181-186, (1997).
8. V.B. Kolmanovskii and V.R. Nosov, Stability of Functional Differential Equations, Academic Press, Orlando, FL, (1986).
9. D.Y. Xu and A. Xu, Domain of attraction of nonlinear functional difference systems, Chinese Science Bulletin 43, 1828-1830, (1998).
10. D.Y. Xu, S.Y. Li, Z.L. Pu and Q.Y. Guo, Domain of attraction of nonlinear discrete systems with delays, Computers Math. Applic. 38 (5/6), 155-162, (1999).
11. D.Y. Xu, Integro-differential equations and delay integral inequalities, Tôhoku Math. J. 44, 365-378, (1992).
12. K. Gopalsamy and X. He, Stability in asymmetric Hopfield nets with transmission delays, Phys. D 76, 344-358, (1994).
13. J.J. Hopfield, Neurons with graded response have collective computational properties like those of two-stage neurons, Proc. Nat. Acad. Sci. U.S.A. 81, 3088-3092, (1984).
14. J.P. Lasalle, The Stability of Dynamical System, SIAM, Philadelphia, (1976).
15. R.A. Horn and C.R. Johnson, Matrix Analysis, World Publishing, Beijing, (1991).