Chaotic dynamics of an integrate-and-fire circuit with periodic pulse-train input

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 50, Issue 5, 2003, Pages 686-693

  Lin, Wei ^a   Ruan, Jiong ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

Chaos; Integrate and fire; Snap back repeller; Symbolic dynamics

Indexed keywords

CAPACITORS; CHAOS THEORY; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; NEURAL NETWORKS; OSCILLATORS (ELECTRONIC); THEOREM PROVING; THRESHOLD VOLTAGE;

INTEGRATE AND FIRE CIRCUIT; PERIODIC PULSE TRAIN INPUT; SNAPBACK REPELLER; SYMBOLIC DYNAMICS;

ELECTRIC NETWORK ANALYSIS;

EID: 0037560993     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2003.811015     Document Type: Article

References (25)

1. J. P. Keener, F. C. Hoppensteadt, and J. Rinzel, "Integrate-and-fire models of nerve membrane response to oscillatory input," SIAM J. Appl. Math., vol. 41, pp. 503-517, 1981.
2. L. Glass and M. C. Mackey, "A simple model for phase locking of biological oscillators," J. Math. Biology, vol. 7, pp. 339-352, 1979.
3. J. J. Hopfield and A. V. M. Herz, "Rapid local synchronization of action potentials: toward computation with coupled integrate-and-fire neurons," Proc. Nat. Acad. Sci., vol. 92, pp. 6655-6662, 1995.
4. R. E. Mirollo and S. H. Strogatz, "Synchronization of pulse-coupled biological oscillators," SIAM J. Appl. Math., vol. 50, no. 6, pp. 1645-1662, 1990.
5. H. Nakano, T. Saito, and K. Mitsubori, "Various impulsive synchronous patterns from mutually coupled ISC chaotic oscillators," in Proc. IEEE ISCAS'99, Orlando, FL, 1999, pp. 475-478.
6. H. Nakano and T. Saito, "Basic dynamics from an integrate-and-fire chaotic circuits with a periodic input," IEICE Trans. Fund., vol. E84-A, no. 5, pp. 1293-1300, 2001.
7. K. Mitsubori and T. Saito, "Mutually pulse-coupled chaotic circuits by using dependent switched capacitors," IEEE Trans. Circuits Syst. I, vol. 47, p. 1469, Oct. 2000.
8. H. Nakano and T. Saito, "Basic dynamics from a pulse-coupled network of autonomous integrate-and-fire chaotic circuits," IEEE Trans. Neural Networks, vol. 12, pp. 92-100, Jan. 2002.
9. K. Miyachi, H. Nakano, and T. Saito, "Response characteristics of a chaotic spiking oscillator," in Proc. IJCNN'02, Honolulu, HI, 2002, pp. 2726-2731.
10. L. Chen and K. Aihara, "Chaos and asymptotical stability in discrete-time neural networks," Phys. D, vol. 104, pp. 286-325, 1997.
11. ____, "Strange attractors in chaotic neural networks," IEEE Trans. Circuits Syst. I, vol. 47, p. 1455, Oct. 2000.
12. G. Chen and X. F. Wang, "On feedback anticontrol of discrete chaos," Int. J. Bifurcation Chaos, vol. 9, no. 7, pp. 1435-1441, 1999.
13. X. F. Wang and G. Chen, "Chaotification via arbitrarily small feedback controls: theory, method, and applications," Int. J. Bifurcation Chaos, vol. 10, no. 3, pp. 59-570, 2000.
14. P. Diamond, "Chaotic behavior of systems of difference equations," Int. J. Syst. Sci., vol. 7, no. 8, pp. 953-956, 1976.
15. n," J. Austr. Math. Soc., ser. A, vol. 31, pp. 217-225, 1981.
16. G. Chen, S. Hsu, and J. Zhou, "Snap-back repellers as a cause of chaotic vibration of the wave equation with a an der Pol boundary condition and energy injection at the middle of the span," J. Math. Phys., vol. 39, no. 12, pp. 6459-6489, 1998.
17. n,", J. Math. Anal. Appl., vol. 63, pp. 199-223, 1978.
18. K. Shiraiwa and M. Kurata, "A generalization of theorem of Marotto," Proc. Japan Acad., vol. 55, pp. 286-289, 1980.
19. D. D. Bainov and P. S. Simeonov, Systems with Impulse Effect: Stability, Theory and Application. Chichester, U.K.: Ellishorwood, 1989.
20. J. Ruan and W. Lin, "Chaos in a class of impulsive differential equation," Com. Non. Sci. Num. Sim., vol. 2, pp. 165-169, 1999.
21. R. L. Devaney, An Introduction to Chaotic Dynamical Systems, 2nd ed. New York: Addison-Wesley, 1989.
22. J. Ruan, L. Juan, and W. Lin, "Dynamics of some neural network models with delay," Phys. Rev. E., vol. 63, pp. 1-11, 2001.
23. W. Lin, J. Ruan, and W. Zhao, "On the mathematical clarification of the snap-back-repeller in high-dimensional systems and chaos in a discrete neural network model," Int. J. Bifurcation Chaos, vol. 12, no. 5, pp. 1129-1140, 2002.
24. W. Lin, "Some theoretical problems in complex systems and their applications," PhD. dissertation, Inst. of Math., Fudan Univ., Shanghai, China, 2002.
25. C. Li and G. Chen, "An improved version of Marotto theorem,", submitted for publication.