Chaotic dynamics of a delayed discrete-time hopfield network of two nonidentical neurons with no self-connections

Journal of Nonlinear Science

Volumn 18, Issue 4, 2008, Pages 415-432

  Kaslik, E ^a   Balint, S ^a  

^a WEST UNIVERSITY OF TIMISOARA   (Romania)

Author keywords

Bifurcation; Chaos; Delays; Neural network; Stability

Indexed keywords

EID: 84867952161     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-007-9015-5     Document Type: Article

References (26)

1. M. Adachi K. Aihara 1997 Associative dynamics in a chaotic neural network Neural Netw. 10 83 98 10.1016/S0893-6080(96)00061-5
2. L. Chen K. Aihara 1995 Chaotic simulated annealing by a neural network model with transient chaos Neural Netw. 8 915 930 10.1016/0893-6080(95)00033-V
3. L. Chen K. Aihara 1997 Chaos and asymptotical stability in discrete-time neural networks Phys. D: Nonlinear Phenom. 104 3-4 286 325 0889.68122 10.1016/S0167-2789(96)00302-8 1453090
4. L. Chen K. Aihara 2001 Chaotic dynamics of neural networks ans its application to combinatorial optimization J. Dyn. Syst. Differ. Equ. 9 3 139 168 05188520 1916868
5. S. Chen C. Shih 2002 Transversal homoclinic orbits in a transiently chaotic neural network Chaos 12 654 671 1080.37611 10.1063/1.1488895 1939457
6. S. Guo L. Huang 2004 Periodic oscillation for discrete-time Hopfield neural networks Phys. Lett. A 329 3 199 206 05272294 10.1016/j.physleta.2004.07. 007 2092277
7. S. Guo L. Huang L. Wang 2004 Exponential stability of discrete-time Hopfield neural networks Comput. Math. Appl. 47 1249 1256 1075.34070 10.1016/S0898-1221(04)90119-8 2070980
8. W. He J. Cao 2007 Stability and bifurcation of a class of discrete-time neural networks Appl. Math. Model. 31 10 2111 2122 05235007 10.1016/j.apm.2006. 08.006
9. J. Hopfield 1982 Neural networks and physical systems with emergent collective computational abilities Proc. Natl. Acad. Sci. 79 2554 2558 10.1073/pnas.79.8.2554 652033
10. Y. Huang X. Zou 2005 Co-existence of chaos and stable periodic orbits in a simple discrete neural network J. Nonlinear Sci. 15 291 303 1098.37069 10.1007/s00332-005-0647-z 2173648
11. E. Kaslik S. Balint 2007 Bifurcation analysis for a two-dimensional delayed discrete-time Hopfield neural network Chaos Solitons Fractals 34 4 1245 1253 10.1016/j.chaos.2006.03.107 2331279
12. Kaslik, E.; Balint, S.: Bifurcation analysis for a discrete-time Hopfield neural network of two neurons with two delays and self-connections. Chaos Solitons Fractals (2007b, in press). doi: 10.1016/j.chaos.2007.01.126
13. Kuznetsov, Y.A.: Elements of Applied Bifurcation Theory. Springer, New York (1998)
14. Y.A. Kuznetsov H. Meijer 2005 Numerical normal forms for codim 2 bifurcations of fixed points with at most two critical eigenvalues. SIAM J. Sci. Comput. 26 1932 1954 1080.37056 10.1137/030601508 2196583
15. C. Li G. Chen 2003 An improved version of the Marotto theorem Chaos Solitons Fractals 18 69 77 1135.37311 10.1016/S0960-0779(02)00605-7 1984552
16. T. Li J. Yorke 1975 Period three implies chaos Am. Math. Mon. 82 985 992 0351.92021 10.2307/2318254 385028
17. n J. Math. Anal. Appl. 63 1 199 233 0381.58004 10.1016/0022-247X(78)90115-4 501175
18. F. Marotto 2005 On redefining a snap-back repeller Chaos Solitons Fractals 25 25 28 1077.37027 10.1016/j.chaos.2004.10.003 2123626
19. Pasemann, F.; Hild, M.; Zahedi, K.: SO(2)-networks as neural oscillators. In: Proceedings IWANN 2003. LNCS, vol. 2686, pp. 144-151. Springer, New York (2003)
20. D. Tank J. Hopfield 1986 Simple neural optimization networks: an A/D converter, signal decision circuit and a linear programming circuit IEEE Trans. Circuits Sys. 33 533 541 10.1109/TCS.1986.1085953
21. H.F. von Bremen F. Udwadia W. Proskurowski 1997 An efficient QR based method for the computation of Lyapunov exponents Phys. D 101 1-2 1 16 0885.65078 1439464
22. W. Yu J. Cao 2006 Cryptography based on delayed chaotic neural networks Phys. Lett. A 356 4-5 333 338 10.1016/j.physleta.2006.03.069
23. Z. Yuan D. Hu L. Huang 2004 Stability and bifurcation analysis on a discrete-time system of two neurons Appl. Math. Lett. 17 1239 1245 1058.92012 10.1016/j.aml.2004.03.004 2099323
24. Z. Yuan D. Hu L. Huang 2005 Stability and bifurcation analysis on a discrete-time neural network J. Comput. Appl. Math. 177 89 100 1063.93030 10.1016/j.cam.2004.09.010 2118661
25. C. Zhang B. Zheng 2005 Hopf bifurcation in numerical approximation of a n-dimension neural network model with multi-delays Chaos Solitons Fractals 25 1 129 146 1136.65326 10.1016/j.chaos.2004.09.099 2123632
26. C. Zhang B. Zheng 2007 Stability and bifurcation of a two-dimension discrete neural network model with multi-delays Chaos Solitons Fractals 31 5 1232 1242 05265048 10.1016/j.chaos.2005.10.074 2262128