Stability and chaos in an inertial two-neuron system

Physica D: Nonlinear Phenomena

Volumn 105, Issue 4, 1997, Pages 267-284

  Wheeler, Diek W ^a   Schieve, W C ^a,b  

^a The University of Texas at Austin   (United States)

^b UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Chaos; Effective neurons; Hopfield model; Inertia; Lyapunov exponent

Indexed keywords

EID: 0038537695     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(97)00008-0     Document Type: Article

References (22)

1. J.J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. National Academy of Sciences (USA) 81 (1984) 3088-3092.
2. W.C. Schieve, A.R. Bulsara and G.M. Davis, Single effective neuron, Phys. Rev. A 43 (1991) 2613-2623.
3. H. Haken, Synergetics (Springer, Berlin, 1977).
4. H. Haken, Advanced Synergetics (Springer, Berlin, 1993).
5. P. Das, W. Schieve and Z. Zeng, Chaos in an effective four-neuron neural netwok, Phys. Lett. A 161 (1991) 60-66.
6. P.K. Das II and William C. Schieve, A bifurcation analysis of the four dimensional generalized Hopfield neural network, Physica D 88 (1995) 14-28.
7. Z. Zeng, W.C. Schieve and P.K. Das, Two neuron dynamics and adiabatic elimination, Physica D 67 (1993) 224-236.
8. K.H. Kwek and J. Li, Periodic solution and dynamics in two neuron network system, Neural Parallel Scientific Comput. 3 (1995) 189-203.
9. K.L. Badcock and R.M. Westervelt, Dynamics of simple electronic neural networks, Physica D 28 (1987) 305-316.
10. J. Tani, Proposal of chaotic steepest descent method for neural networks and analysis of their dynamics, Electron. Comm. Japan 75 (4) (1992) 62-70.
11. J. Tani and M. Fujita, Coupling of memory search and mental rotation by a nonequilibrium dynamics neural network, IEICE Trans. Fund. Electron., Commun. Comput. Sci. E75-A (5) (1992) 578-585.
12. J. Tani, Model-based learning for mobile robot navigation from the dynamical systems perspective, IEEE Trans. Systems Man Cybernet. 26 (3) (1996) 421-436.
13. J.F. Ashmore and D. Attwell, Models for electrical tuning in hair cells, Proc. Royal Soc. London B 226 (1985) 325-344.
14. D.E. Angelaki and M.J. Correia, Models of membrane resonance in pigeon semicircular canal type II hair cells, Biol. Cybernet. 65 (1991) 1-10.
15. A. Mauro, F. Conti, F. Dodge and R. Schor, Subthreshold behavior and phenomenological impedance of the squid giant axon, J. General Physiol. 55 (1970) 497-523.
16. ++ conductance in membrane resonance of trigeminal root ganglion neurons, J. Neurophysiology 59 (1) (1988) 77-89.
17. C. Koch, Cable theory in neurons with active, linearized membranes, Biol. Cybernet. 50 (1984) 15-33.
18. S. Rader, D.W. Wheeler, W.C. Schieve and P. Das, Nonlinear resonance in neuron dynamics, Z. Naturf. A 50 (1995) 718-726.
19. A.A. Andronov, A.A. Vitt and S.E. Khaikin, Theory of Oscillators (Pergamon Press, Oxford, 1966).
20. F. Verhulst, Nonlinear Differential Equations and Dynamical Systems (Springer, Berlin, 1990).
21. H. Matsuda and A. Uchiyama, A neural network model for gererating intermittent chaos, IEICE Trans. Fund. Electron. Commun. Comput. Sci. E76 A (9) (1993) 1544-1547.
22. C.M. Marcus, F.R. Waugh and R.M. Westervelt, Nonlinear dynamics and stability of analog neural networks, Physica D 51 (1991) 234-247.