Abstract
In this paper we consider the Bonhoeffer-van der Pol (BVP) equation which describes propagation of nerve pulses in a neural membrane, and characterize the chaotic attractor at various bifurcations, and the probability distribution associated with weak and strong chaos. We illustrate control of chaos in the BVP equation by the Ott-Grebogi-Yorke method as well as through a periodic instantaneous burst.
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References
H G Schüster,Deterministic chaos (Verlag Chemie, Weinheim, 1988)
M Lakshmanan and K Murali,Chaos in nonlinear oscillators: controlling and synchronization (World Scientific, Singapore, 1996)
H D I Abarbanel, R Brown and M B Kennel,J. Nonlinear. Sci. 1, 175 (1991)
C Amitrano and R S Berry,Phys. Rev. E47, 3158 (1993)
N Voglis and G J Contopoulos,J. Phys. A27, 4899 (1994)
J L Chern and K Otsuka,Phys. Lett. A188, 321 (1994)
S K Nayak, R Ramaswamy and C Chakravarty,Phys. Rev. E51, 3376 (1995)
S Rajasekar,Indian J. Phys. B70, 51 (1996)
R Ishizaki, T Horita and H Mori,Prog. Theor. Phys. 89, 947 (1993)
H Hate, T Horita and H Mori,Prog. Theor. Phys. 82, 897 (1989)
T Horita and H Mori,Prog. Theor. Phys. 91, 677 (1994)
S Rajasekar,Phys. Rev. E52, 3234 (1995)
S Rajasekar,Chaos, Solitons and Fractals (1996, in press)
P Philominathan and S Rajasekar,Physica 229, 244 (1996)
J L Chern and T C Chow,Phys. Lett. A192, 34 (1994)
S Rajasekar,Characteristics of probability distribution in chaos in an one dimensional map and BVP oscillator (in preparation)
E Ott, C Grebogi and J Yorke,Phys. Rev. Lett. 64, 1196 (1990)
B A Huberman and E Lumer,IEEE Trans. Circuits Syst. 37, 547 (1990)
S Sinha, R Ramaswamy and J Subba Rao,Physica D43, 118 (1990)
R Lima and M Pettini,Phys. Rev. A41, 726 (1990)
J Singer, Y Z Wang and H H Bau,Phys. Rev. Lett. 66, 1123 (1991)
K Pyragas,Phys. Lett. A170, 421 (1992)
G Chen and X Dong,Int. J. Bifur. Chaos 2, 407 (1992)
Y Braiman and I Goldhirsch,Phys. Rev. Lett. 66, 2545 (1991)
A Hübler and E Luscher,Naturwissenschaften 76, 67 (1989)
E A Jackson,Phys. Rev. A44, 4839 (1991)
S Rajasekar and M Lakshmanan,Int. J. Bifur. Chaos 2, 201 (1992)
S Rajasekar and M Lakshmanan,Physica D67, 282 (1993)
S Rajasekar and M Lakshmanan,J. Theor. Biol. 166, 275 (1994)
S Rajasekar,Pramana — J. Phys.,41, 295 (1993)
S Rajasekar,Chaos, solitons and fractals,5, 2135 (1995)
S Rajasekar,Phys. Rev. E51, 775 (1995)
S Rajasekar,Controlling of chaos by periodic instantaneous burst (submitted for publication)
J K John and R E Amritkar,Int. J. Bifur. Chaos 4, 1687 (1994)
J K John and R E Amritkar,Phys. Rev. E49, 4843 (1994)
K Murali and M Lakshmanan,J. Circuits Systems and Computers 3, 125 (1993)
S Parthasarathy and S Sinha,Phys. Rev. E51, 6239 (1995)
S D Gadre and V S Varma,Pramana — J. Phys. 45, 355 (1995)
G Chen and X Dong,Int. J. Bifur. Chaos 3, 1363 (1993)
L M Pecora and T L Carroll,Phys. Rev. Lett. 64, 821 (1990)
R E Amritkar and Neelima Gupte,Phys. Rev. A44, 3403 (1991)
Neelima Gupte and R E Amritkar,Phys. Rev. E48, R1620 (1993)
R E Amritkar and Neelima Gupte,Phys. Rev. E47, 3889 (1993)
K Murali and M Lakshmanan,Phys. Rev. E48, R1624 (1993)
K Murali, M Lakshmanan and L O Chua,Int. J. Bifur. Chaos 5, 563 (1995)
A C Scott,Neurophysics (Wiley, New York, 1977)
S Rajasekar and M Lakshmanan,Physica D32, 146 (1988)
S Rajasekar, S Parthasarathy and M Lakshmanan,Chaos, Solitons and Fractals 2, 271 (1992)
P M Gade and R E Amritkar,Phys. Rev. A45, 725 (1992)
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Rajasekar, S. Characterization and control of chaotic dynamics in a nerve conduction model equation. Pramana - J Phys 48, 249–258 (1997). https://doi.org/10.1007/BF02845633
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DOI: https://doi.org/10.1007/BF02845633