Existence and Exponential Stability of Anti-periodic Solutions for a High-Order Delayed Cohen–Grossberg Neural Networks with Impulsive Effects

Neural Processing Letters

Volumn 40, Issue 3, 2014, Pages 227-243

  Xu, Changjin ^a   Zhang, Qiming ^b  

^a GUIZHOU UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^b HUNAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Anti periodic solution; Exponentially stability; High order Cohen Grossberg neural networks; Impulse; Time varying delay

Indexed keywords

STABILITY CRITERIA;

ANTI-PERIODIC SOLUTIONS; EXPONENTIALLY STABILITIES; HIGH-ORDER; IMPULSE; TIME VARYING- DELAYS;

NEURAL NETWORKS;

EID: 84912093708     PISSN: 13704621     EISSN: 1573773X     Source Type: Journal    
DOI: 10.1007/s11063-013-9325-6     Document Type: Article

References (44)

1. Cohen MA, Grossberg S (1983) Absolute stability of global pattern formation and parallel memory by competetive neural networks. IEEE Trans Syst Man Cybern 13:815–826
2. Cao J, Wang J (2005) Global exponential stability and periodicity of recurrent neural networks with time delays. IEEE Trans Circuits Syst I 52(5):920–931
3. Chen Z, Zhao DH, Ruan J (2007) Dynamic analysis of high order Cohen–Grossberg neural networks with time delay. Chaos Solitons Fractals 32(4):1538–1546
4. Chen Z, Zhao D, Fu X (2009) Discrete analogue of high-order periodic Cohen–Grossberg neural networks with delay. Appl Math Comput 214(1):210–217
5. Wu C, Ruan J, Lin W (2006) On the existence and stability of the periodic solution in the Cohen–Grossberg neural network with time delay and high-order terms. Appl Math Comput 177(1):194–210
6. Zhang ZQ, Liu WB, Zhou DM (2012) Global asymptotic stability to a generalized Cohen–Grossberg BAM neural networks of neutral type delays. Neural Netw 25:94–105
7. Xu BJ, Liu XZ, Liao XX (2006) Global exponential stability of high order Hopfield type neural networks. Appl Math Comput 174(1):98–116
8. Xu BJ, Liu XZ, Liao XX (2003) Global exponential stability of high order Hopfield type neural networks with time delays. Comput Math Appl 45(10–11):1729–1737
9. Wu W, Cui BT (2008) Global robust exponential stability of delayed neural networks. Chaos Solitons Fractals 35(4):747–754
10. Zeng ZG, Wang J (2006) Improved conditions for global exponential stability of recurrent neural networks with time-varying delays. IEEE Trans Neural Netw 17(3):623–635
11. Chen Z, Ruan J (2005) Global stability analysis of impulsive Cohen–Grossberg neural networks with delay. Phys Lett A 345(1–3):101–111
12. Cao JD, Liang JL, Lam J (2004) Exponential stability of high-order bidirectional associative memory neural networks with time delays. Phys D 199(3–4):425–436
13. Ren FL, Cao JD (2007) Periodic solutions for a class of higher-order Cohen–Grossberg type neural networks with delays. Comput Math Appl 54(6):826–839
14. Li YK, Yang L (2009) Anti-periodic solutions for Cohen–Grossberg neural netowrks with bounded and unbounded dealys. Commun Nonlinear Sci Numer Simul 14(7):3134–3140
15. Shao JY (2008) Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays. Phys Lett A 372(30):5011–5016
16. Fan QY, Wang WT, Yi XJ (2009) Anti-periodic solutions for a class of nonlinear $$n$$nth-order differential equations with delays. J Comput Appl Math 230(2):762–769
17. Li YK, Xu EL, Zhang TW (2010) Existence and stability of anti-periodic solution for a class of generalized neural networks with impulsives and arbitrary delays on time scales. J Inequal Appl 2010:19 Article ID 132790
18. Aftabizadeh AR, Aizicovici S, Pavel NH (1992) On a class of second-order anti-periodic boundary value problems. J Math Anal Appl 171(2):301–320
19. Aizicovici S, McKibben M, Reich S (2001) Anti-periodic solutions to nonmonotone evolution equations with discontinuous nonlinearities. Nonlinear Anal Theory Methods Appl 43(2):233–251
20. Gong SH (2009) Anti-periodic solutions for a class of Cohen–Grossberg neural networks. Comput Math Appl 58(2):341–347
21. Liu BW (2009) An anti-periodic LaSalle oscillation theorem for a class of functional differential equations. J Comput Appl Math 223(2):1081–1086
22. Ou CX (2008) Anti-periodic solutions for high-order Hopfield neural networks. Comput Math Appl 56(7):1838–1844
23. Peng GQ, Huang LH (2009) Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Nonlinear Anal Real World Appl 10(40):2434–2440
24. Huang ZD, Peng LQ, Xu M (2010) Anti-periodic solutions for high-order cellular neural netowrks with time-varying delays. Electr J Differ Equ 2010(5):1–9
25. Zhang AP (2013) Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays. Adv Differ Equ 162 (in press)
26. Li YK, Yang L, Wu WQ (2011) Anti-periodic solutions for a class of Cohen–Grossberg neural networks with time-varying on time scales. Int J Syst Sci 42(7):1127–1132
27. Pan LJ, Cao JD (2011) Anti-periodic solution for delayed cellular neural networks with impulsive effects. Nonlinear Anal Real World Appl 12(6):3014–3027
28. Li YK (2011) Anti-periodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales. Commun Nonlinear Sci Numer Simul 16(8):3326–3336
29. Fan QY, Wang WT, Yi XJ, Huang LH (2011) Anti-periodic solutions for a class of third-order nonlinear differential equations with deviating argument. Electr J Qual Theory Differ Equ 8(12):1–12
30. Wang W, Shen J (2009) Existence of solutions for anti-periodic boundary value problems. Nonliear Anal 70(2):598–605
31. Chen YQ, Nieto JJ, O’Regan D (2007) Anti-periodic solutions for fully nonlinear first-order differential equations. Math Comput Model 46(9–10):1183–1190
32. Peng L, Wang WT (2013) Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays in leakage terms. Neurocomputing 111:27–33
33. Park JY, Ha TG (2009) Existence of anti-periodic solutions for quasilinear parabolic hemivariational inequalities. Nonlinear Anal Theory Methods Appl 71(7–8):3203–3217
34. Yu YH, Shao JY, Yue GX (2009) Existence and uniqueness of anti-periodic solutions for a kind of Rayleigh equation with two deviating arguments. Nonlinear Anal Theory Methods Appl 71(10):4689–4695
35. Lv X, Yan P, Liu DJ (2010) Anti-periodic solutions for a class of nonlinear second-order Rayleigh equations with delays. Commun Nonlinear Sci Numer Simul 15(11):3593–3598
36. Li YQ, Huang LH (2009) Anti-periodic solutions for a class of Linard-type systems with continuously distributed delays. Nonlinear Anal Real World Appl 10(4):2127–2132
37. Liu BW (2009) Anti-periodic solutions for forced Rayleigh-type equations. Nonlinear Anal Real World Appl 10(5):2850–2856
38. Shi PL, Dong LZ (2010) Existence and exponential stability of anti-periodic solutions of Hopfield neural networks with impulses. Appl Math Comput 216(2):623–630
39. Chen Z, Fu XL, Zhao DH (2013) Anti-periodic mild attractor of delayed Hopfield neural networks systems with reaction-diffusion terms. Neurocomputing 99:372–380
40. Balasubramaniam P, Vembarasan V, Rakkiyappan R (2012) Global robust asymptotic stability analysis of uncertain switched Hopfield neural networks with time delay in the leakage term. Neural Comput Appl 21(7):1593–1616
41. Balasubramaniam P, Vembarasan V (2011) Global asymptotic stability results for BAM neural networks of neutral-type with time delays in the leakage term under impulsive perturbations. Int J Comput Math 88(15):3271–3291
42. Chen ZB (2012) A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput Appl. doi:10.1007/s00521-012-1200-2
43. Zhang AP (2013) Existence and exponential stability of anti-periodic solutions for HCNNs with time-varying leakage delays. Adv Differ Equ 2013:162. doi:10.1186/1687-1847-2013-162
44. Liu BW, Gong SH (2013) Periodic solution for impulsive cellar neural networks with time-varying delays in the leakage terms. Abstr Appl Anal 2013:10 Article ID 701087