Analysis of bifurcation phenomena in a 3-cells hysteresis neural network

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

Volumn 46, Issue 7, 1999, Pages 851-857

  Jin'No, Kenya ^a   Nakamura, Takahiko ^b   Saito, Toshimichi ^c  

^a NIPPON INSTITUTE OF TECHNOLOGY   (Japan)

^b RISO Laboratory Inc   (Japan)

^c HOSEI UNIVERSITY   (Japan)

Author keywords

Bifurcation; Chaos; Coupled oscillator; Hysteresis; Piecewise linear system

Indexed keywords

BIFURCATION (MATHEMATICS); CHAOS THEORY; HYSTERESIS; MATHEMATICAL MODELS; OSCILLATORS (ELECTRONIC); PIECEWISE LINEAR TECHNIQUES;

CONTROL PARAMETERS; COUPLED OSCILLATOR; PERIODIC ORBITS;

NEURAL NETWORKS;

EID: 0032641422     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/81.774231     Document Type: Article

References (14)

1. R. Hecht-Nielsen, Neurocomputing. Reading, MA: Addison-Wesley, 1990.
2. J. J. Hopfield, Neural networks and physical systems with emergent collective computational abilities, in Proc. Nat. Acad. Sei. USA, vol. 79, pp. 2554-2558, Apr. 1982.
3. H. Kawakami, Bifurcation of periodic responses in forced dynamic nonlinear circuits: Computation of bifurcation values of the system parameters, IEEE Trans. Circuits Syst., vol. CAS-31, pp. 248-260, Mar. 1984.
4. F. Chapeau-Blondeau and G. Chauvet, Stable, oscillatory, and chaotic regimes in the dynamics of small neural networks with delay, Neural Networks, vol. 5, no. 5, pp. 735-743, 1992.
5. F. Pasemann, Characterization of periodic attractors in neural ring networks, Neural Networks, vol. 8, no. 3, pp. 421129, 1995.
6. K. Jin'no and T. Saito, Analysis and synthesis of a continuous-time hysteresis neural network, in Proc. 1992 IEEE Int. Symp. Circuits Systems (ISCAS'92), San Diego, CA, 1992, pp. 47174.
7. _, Obtaining an ideal associative memory by means of a simple hysteresis network, Electron, and Commun. Jpn., pt. 3, vol. 78, no. 9, pp. 76-85, 1995.
8. T. Saito and M. Oikawa, Chaos and fractals from a forced artificial neural cell, IEEE Trans. Neural Networks, vol. 4, no. 1, pp. 43-52, 1993.
9. T. Saito and Y. Matsumoto, Chaos, torus, and synchronization from three coupled relaxation oscillators, IEEE Trans. Circuits Syst., vol. 41, pp. 754-759, Nov. 1994.
10. K. Jin'no, Chaos and related bifurcation phenomena from a simple hysteresis network, IEICE Trans. Fundamentals, vol. E79-A, no. 3, pp. 40214, 1996.
11. K. Jin'no and T. Saito, Analysis of periodic attractors from a simple hysteresis network, IEICE Trans. Fundamentals, vol. E79-A, no. 6, pp. 873-882, 1996.
12. O. E. Rössler, An equation for hyperchaos, Phys. Lett. A, vol. 71, pp. 155-157, 1979.
13. J. D. Farmer, E. Ott, and J. A. Yorke, The dimension of chaotic attractors, Physica 7D, 1983, pp. 153-180.
14. K. Jin'no and M. Tanaka, Hysteresis quantizer, in Proc. 1997 IEEE Int. Symp. Circuits Systems (ISCAS'97), Hong Kong, 1997, pp. 661-664.