Analog realization of arbitrary one-dimensional maps

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

Volumn 50, Issue 12, 2003, Pages 1538-1547

  Del Moral Hernandez, Emilio ^a   Lee, Geehyuk ^b,c   Farhat, Nabil H ^b  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

^c Korea Advanced Institute of Science and Technology (KAIST)   (South Korea)

Author keywords

Bifurcating neuron (BN); Coupled map lattice; Neural network; One dimensional (1 D) map; Parametrically coupled map lattice (PCML)

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL COMPLEXITY; IMAGE PROCESSING; IMAGING SYSTEMS; MATHEMATICAL MODELS; MATHEMATICAL PROGRAMMING; ONE DIMENSIONAL; OSCILLATORS (ELECTRONIC); TRANSISTORS;

BIFURCATING NEURON; INTEGRATED CIRCUIT RELAXATION OSCILLATOR NEURON; ONE DIMENSIONAL MAP; PARAMETRICALLY COUPLED MAP LATTICE; PROGRAMMABLE UNIJUNCTION TRANSISTOR OSCILLATOR NEURON; SECURE COMMUNICATION SYSTEMS;

NEURAL NETWORKS;

EID: 0742286816     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2003.819805     Document Type: Article

References (48)

1. R. M. May, "Simple mathematical models with very complicated dynamics," Nature, vol. 26, pp. 459-467, 1976.
2. R. Perez and L. Glass, "Bistability period-doubling bifurcation and chaos in periodically forced oscillator," Phys. Lett. A, vol. 90, pp. 441-443, 1982.
3. M. H. Jensen, P. Bak, and R. Bohr, "Transition to chaos by interaction of resonances in dissipative systems. I. Circle maps," Phys. Rev. A, vol. 30, pp. 1960-1969, 1984.
4. R. Bohr, P. Bak, and M. H. Jensen, "Transition to chaos by interaction of resonances in dissipative systems. II. Josephson junctions, charge-density waves, and standard maps," Phys. Rev. A, vol. 30, pp. 1970-1981, 1984.
5. A. S. Pikovsky, "A dynamical model for periodic and chaotic oscillations in the Belousov-Zhabotinsky reaction," Phys. Lett. A, vol. 85, no. 1, pp. 13-16, 1981.
6. R. H. Simoyi, A. Wolf, and H. L. Swinney, "One-dimensional dynamics in a multicomponent chemical reaction," Phys. Rev. Lett., vol. 49, no. 4, pp. 245-248, 1982.
7. F. Papoff, A. Fioretti, and E. Arimondo, "Return maps for intensity and time in a homoclinic-chaos model applied to a laser with a saturable absorber," Phys. Rev. A, vol. 44, no. 7, pp. 4639-4651, 1991.
8. N. H. Farhat and M. Eldefrawy, "The bifurcating neuron," in Dig. Ann. OSA Meeting, San Jose, CA, 1991, pp. 10-10.
9. ____, "The bifurcating neuron: characterization and dynamics," in Photonics for Computers, Neural Networks, and Memories. San Diego, CA: SPIE, July 1992, vol. 1773, pp. 23-34.
10. N. H. Farhat, S.-Y. Lin, and M. Eldefrawy, "Complexity and chaotic dynamics in a spiking neuron embodiment," in Adaptive Computing: Mathematics, Electronics, and Optics. Orlando, FL: Society of Photo-Optical Instrumentation Engineers, Apr. 1994, vol. 55, pp. 77-88.
11. S.-Y. Lin, "Synchronicity and coherence in artificial neural networks," Ph.D. dissertation, Elect. Eng. Dep., Univ. Pennsylvania, Philadelphia, 1994.
12. M. Zeller, M. Bauer, and W. Martienssen, "Neural dynamics modeled by one-dimensional circle maps," Chaos, Solitons, Fractals, vol. 5, no. 6, pp. 885-893, 1995.
13. P. A. Anninos, B. Beek, T. J. Csermely, E. M. Harth, and G. Pertile, "Dynamics of neural structures," J. Theor. Biol., vol. 26, pp. 121-148, 1970.
14. E. Harth, "Order and chaos in neural systems: an approach to the dynamics of higher brain functions," IEEE Trans. Syst., Man, Cybern., vol. SMC-13, no. 5, pp. 782-789, 1983.
15. M. Usher, H. G. Schuster, and E. Neibur, "Dynamics of populations of integrated-and-fire neurons, partial synchronization and memory," Neural Computation, vol. 5, pp. 570-586, 1993.
16. K. Kaneko, "Overview of coupled map lattices," Chaos, vol. 2, no. 3, pp. 279-282, 1992.
17. H. Nozawa, "A neural network model as a globally coupled map and applications based on chaos," Chaos, vol. 2, no. 3, pp. 377-386, 1992.
18. M. Inoue and A. Nagayoshi, "A chaos neuro-computer," Phys. Rev. A, vol. 158, pp. 373-376, 1991.
19. C. B. Price, P. Wambacq, and A. Oosterlinck, "The plastic coupled map lattice: a novel image-processing paradigm," Chaos, vol. 2, no. 3, pp. 351-366, 1992.
20. A. V. Oppenheim, G. W. Wornell, S. H. Isabelle, and K. M. Cuomo, "Signal processing in the context of chaotic signals," in Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing, vol. 4, 1992, pp. 117-120.
21. G. Heidari-Bateni and C. D. McGillem, "A chaotic direct-sequence spread-spectrum communication system," IEEE Trans. Commun., vol. 42, pp. 1524-1527, Feb. 1994.
22. B. Chen and G. W. Wornell, "Efficient channel coding for analog sources using chaotic systems," in Proc. IEEE Global Telecommunications Conf., Nov., 18-22 1996, vol. 1, pp. 131-135.
23. G. Hu, J. Xiao, J. Yang, F. Xie, and Z. Qu, "Synchronization of spatiotemporal chaos and its applications," Phys. Rev. E, vol. 56, no. 3, pp. 2738-2746, 1997.
24. K. Kaneko, Theory and Applications of Coupled Map Lattices. Chichester, U.K.: Wiley, 1993.
25. E. Del Moral Hernandez, "Artificial neural networks based on bifurcating recursive processing elements," Ph.D. dissertation, Elect. Eng. Dep., Univ. Pennsylvania, Philadelphia, 1998.
26. N. H. Farhat and E. Del Moral Hernandez, "Logistic networks with DNA-like encoding and interactions," in Lecture Notes in Computer Science. Berlin, Germany: Springer-Verlag, 1995, vol. 930, pp. 214-222.
27. ____, "Recurrent networks with recursive processing elements: a paradigm for dynamical computing," in Proc. SPIE, vol. 2824, Denver, CO, 1996, pp. 158-170.
28. N. H. Farhat, E. D. M. Hernandez, and G. Lee, "Strategies for autonomous adaptation and learning in dynamical networks," in Proc. Int. Work Conf. Artificial Natural Neural Networks, Lanzarote, Spain, 1997.
29. N. Farhat, G. Lee, and X. Ling, "Dynamical networks for ATR," in Proc. RTO Meeting 6: Non-Cooperative Air Target Identification Using Radar, Nov. 1998, pp. D-1-D-9.
30. N. H. Farhat and M. Eldefrawy, "Complexity and chaotic dynamics in a photonic neuron embodiment," in Proc. 1st Symp. Nonlinear Theory Applications, vol. 1, Dec. 1993, pp. 91-97.
31. A. V. Holden and S. M. Ramadan, "The response of a molluscan neuron to a cyclic input: entrainment and phase-locking," Biol. Cybern., vol. 41, pp. 157-163, 1981.
32. A. V. Holden, W. Winlow, and P. G. Haydon, "The induction of periodic and chaotic activity in a molluscan neuron," Biol. Cybern., vol. 43, pp. 169-173, 1982.
33. K. Aihara and G. Matsumoto, "Chaotic oscillations and bifurcations in squid giant axons," in Chaos, A. V. Holden, Ed: Princeton University Press, 1986, pp. 257-269.
34. S. M. Sze, Physics of Semiconductor Devices, 2nd ed. New York: Wiley, 1981.
35. R. K. Sugandhi, Thyristors, Theory and Applications, 2nd ed. New York: Wiley, 1984.
36. L. Trajkovic and J. A. N. Willson, "Complementary two-transistor circuits and negative differential resistance," IEEE Trans. Circuits Syst., vol. 37, pp. 1258-1265, 1990.
37. A. S. Baek, "Pulse-Coupled networks: dynamics, applications, and implementations," Ph.D. dissertation, Elect. Eng. Dep., Univ. Pennsylvania, Philadelphia, 1997.
38. M. P. Kennedy and L. O. Chua, "van der pol and chaos," IEEE Trans. Circuits Syst., vol. 44, pp. 974-980, 1997.
39. R. C. Hilborn, Chaos and Nonlinear Dynamics, An Introduction for Scientists and Engineers. New York: Oxford Univ. Press, 1994.
40. AN-372: Application Note 372 Designer's Encyclopedia of Bipolar One-Shots, F. S. Corporation. (1998, Apr.). [Online]. Available: http://www.fairchildsemi.com
41. MicroSim, MicroSim PSpice and Basics: User's Guide, MicroSim Corp., San Jose, CA, 1997.
42. LM555/LM555C Timer, N. S. Corporation, (1997, May). [Online]. Available: http://www.national.com
43. H. Torikai and T. Saito, "A multiplex communication system using chaotic pulse-train with sawtooth control," in Proc. IEEE Int. Symp. Circuits Systems, vol. 2, 1997, pp. 1065-1068.
44. ____, "Return map quantization from an integrate-and-fire model with two periodic inputs," IEICE Trans. Fund., vol. E82-A, no. 7, pp. 1336-1343, 1999.
45. ____, "Resonance phenomenon of interspike intervals from an integrate-and-fire model with two periodic inputs," IEEE Trans. Circuits Syst. I, vol. 48, pp. 1198-1204, Oct. 2001.
46. T. Moire, S. Sakbayashi, M. Nagata, and A. Iwaty, "Cmos circuits generating arbitrary chaos by using pulse-width modulation techniques," IEEE Trans. Circuits Syst. I, vol. 47, pp. 1652-1657, Nov. 2000.
47. M. Delgado-Restito and A. Rodriguez-Vazquez, "Integrated chaos generator," Proc. IEEE, vol. 90, pp. 747-767, May 2002.
48. N. H. Farhat and M. Eldefrawy, Proc. Int. Symp. on Nonlinear Theory and Applications, vol. 1, Dec. 1993, pp. 91-97.