Propagation of periodic and chaotic action potential trains along nerve fibers

Physica D: Nonlinear Phenomena

Volumn 100, Issue 1-2, 1997, Pages 212-224

  Jianxue, Xu ^a   Yunfan, Gong ^a   Wei, Ren ^b   Sanjue, Hu ^b   Fuzhou, Wang ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b FOURTH MILITARY MEDICAL UNIVERSITY   (China)

Author keywords

Chaos; ISI time series; Largest Lyapunov exponent; Neural electrophysiological activities; Nonlinear forecasting method; The surrogate data

Indexed keywords

EID: 22244447809     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(96)00188-1     Document Type: Article

References (46)

1. A.L. Hodgkin and A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. (London) 117 (1952) 500.
2. A.C. Scott, The electrophysics of a nerve fiber, Rev. Modern Phys. 47 (1975) 487.
3. T.R. Chay, Electrical bursting and intracellular calcium ion oscillations in excitable cell models, Biol. Cybern. 63 (1990) 15.
4. P. Lansky and J.P. Rospars, Ornstein-Uhlenbeck model neuron revisited, Biol. Cybern. 72 (1995) 397.
5. L.J. Bruner and J.R. Harvey, The spike generation zone of the ampullary electroreceptor. I. Stimulus-response characteristics of a relaxation oscillator circuit model, Biol. Cybern. 72 (1995) 371.
6. K. Aihara and G. Matsumoto, Chaotic oscillations and bifurcations in squid giant axons, in: Chaos, Nonlinear Science: Theory and Applications, ed. A.V. Holden (Manchester University Press, Manchester, 1985) p. 257.
7. G. Matsumoto, K. Aihara and T. Utsunomiya, A spatially ordered pacemaker observed in squid giant axons, J. Phys. Soc. Japan 51 (1982) 942.
8. K. Aihara, G. Matsumoto and M. Ichiwaka, An alternating periodic-chaotic sequence observed in neural oscillations, Phys. Lett. A 111 (1985) 251.
9. P.E. Rapp, I.D. Zimmerman, A.M. Albano, G.C. Deguzman and N.N. Greenbaun, Dynamics of spontaneous neural activity in the simian motor cortex: the dimension of chaotic neurons, Phys. Lett. A 110 (1985) 335.
10. T. Elbert, W.J. Zbigniew, J. Kowalik, J.E. Skinner, K.E. Graf and N. Birbaumer, Chaos and physiology: deterministic chaos in excitable cell assemblies, Physiol. Rev. 74 (1994) 1.
11. N.H. Packard, J.P. Crutchfield, J.D. Farmer and R.S. Shaw, Geometry from a time series, Phys. Rev. Lett. 45 (1980) 712.
12. F. Takens, Detecting strange attractors in turbulence, in: Lecture Notes in Mathematics 898, eds. D.A. Rand and L.-S. Yong (Springer, Berlin, 1981) p. 366.
13. P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys. Rev. Lett. 50 (1983) 346.
14. P. Grassberger and I. Procaccia, Measuring the strangeness of strange attractors, Physica D 9 (1983) 189.
15. A. Ben-Mizrachi, I. Procaccia and P. Grassberger, The characterization of experimental (noisy) strange attractor, Phys. Rev. A 29 (1984) 975.
16. P. Grassberger, Do climatic attractors exist?, Nature 323 (1986) 609.
17. A.R. Osborne and A. Provenzale, Finite correlation dimension for stochastic systems with power-law spectra, Physica D 35 (1989) 357.
18. G. Sugihara and R.M. May, Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series, Nature 344 (1990) 734.
19. Xu Jianxue, Gong Yunfan, Ren Wei, Hu Sanjue and Wang Fuzhou, Application of nonlinear forecasting method to the analysis of interspike intervals in nervous system, Acta Biophysica Sinica, accepted.
20. E. Ott, T. Sauer and J.A. Yorke (eds.) Coping With Chaos (Wiley, New York, 1994).
21. P. Cvitanovic, Periodic orbits as the skeleton of classical and quantum chaos, Physica D 51 (1991) 138.
22. P. Cvitanovic, Invariant measurement of strange sets in terms of cycles, Phys. Rev. Lett. 61 (1988) 2729.
23. D. Auerbach, P. Cvitanovic, J.-P. Eckmann, G. Gunaratne and I. Procaccia, Exploring chaotic motion through periodic orbits, Phys. Rev. Lett. 58 (1987) 2387.
24. D. Pierson and F. Moss, Detecting periodic unstable points in noisy chaotic and limit cycle attractors with applications to biology, Phys. Rev. Lett. 75 (1995) 2124.
25. G.J. Bennett and Y.-K. Xie, A peripheral mononeuropathy in rat that produces disorders of pain sensation like those seen in man, Pain 33 (1988) 87.
26. D. Sigeti and W. Horsthemke, High-frequency power spectra for systems subject to noise, Phys. Rev. A 35 (1987) 2276.
27. Xu Jianxue, Gong Yunfan, Ren Wei, Hu Sanjue and Wang Fuzhou, Bifurcation and chaos phenomenon of interspike intervals in nervous system, in: Conf. on Nonlinearity, Bifurcation, Chaos: the Doors to the Future (Poland, September 1996) accepted.
28. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian and J.D. Farmer, Testing for nonlinearity in time series: the method of surrogate data, Physica D 58 (1992) 77.
29. J. Rinzel, A. Sherman and C.L. Stokes, Channels, coupling, and synchronized rhythmic bursting activity, in: Analysis and Modeling of Neural Systems, ed. F.H. Eeckman (Kluwer Academic Publishers, Dordrecht, 1989) p. 29.
30. D.S. Broomhead and G.P. King, Extracting qualitative dynamics from experimental data, Physica D 20 (1986) 217.
31. R.M. May, Simple mathematical models with very complicated dynamics, Nature 261 (1976) 459.
32. J.-C. Roux, R.H. Simoyi and H.L. Swinney, Observation of a strange attractor, Physica D 8 (1983) 257.
33. H.L. Swinney, Experimental observations of order and chaos, in: Nonlinear Dynamics and Chaos, eds. J.M.T. Thompson and H.B. Stewart (Wiley, New York, 1986) p. 232.
34. F.C. Moon, Chaotic and Fractal Dynamics (Wiley, New York, 1992) p. 110.
35. A.N. Sarkovskii, Coexistence of cycles of a continuous map of a line into itself, Ukrainian J. Math. 16 (1964) 61.
36. T.-Y. Li and J.A. Yorke, Period three implies chaos, Amer. Math. Monthly 82 (1975) 985.
37. A. Wolf, J.B. Swift, H.L. Swinney and J.A. Vastano, Determining Lyapunov exponents from a time series, Physica D 16 (1985) 285.
38. A. Wolf, Quantifying chaos with Lyapunov exponents, in: Chaos, ed. A.V. Holden (Manchester University Press, Manchester, 1986) p. 273.
39. Y.S. Fan and T.R. Chay, Generation of periodic and chaotic bursting in an excitable cell model, Biol. Cybern. 71 (1994) 417.
40. Gong Yunfan, Xu Jianxue, Ren Wei, Hu Sanjue and Wang Fuzhou, Observing nonlinear phenomena in nervous system: from theory to experimental realization, to be submitted.
41. J.M. Gilchrist, M. Perrone and J. Ross, Dynamical analysis of neuromuscular transmission jitter, Muscle-Nerve 18 (1995) 685.
42. Gong Yunfan, Xu Jianxue, Ren Wei, Hu Sanjue and Wang Fuzhou, Determine the degree of chaos from the analysis of ISI time series in nervous system: a comparison between the correlation dimension and the nonlinear forecasting method, to be submitted.
43. D.J. Wales, Calculating the rate of loss of information from chaotic time series by forecasting, Nature 350 (1991) 485.
44. Gong Yunfan, Xu Jianxue, Ren Wei, Hu Sanjue and Wang Fuzhou, Bifurcation: the mechanism underlying the delayed feedback method and its applications to the control of neural chaotic bursting, Physica D, submitted.
45. Gong Yunfan, Xu Jianxue, Ren Wei, Hu Sanjue and Wang Fuzhou, Bifurcation chaos and control in nervous system, Acta Biophysica Sinica, accepted.
46. M. Bushev, Synergetics: Chaos, Order, Self-organization (World Scientific, Singapore, 1994) p. 61.