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Volumn 7, Issue 12, 1997, Pages 2653-2689

Numerical studies of the periodically forced Bonhoeffer van der Pol system

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EID: 0031537174     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497001801     Document Type: Review
Times cited : (27)

References (39)
  • 1
    • 33847575273 scopus 로고
    • The Devil's staircase
    • Bak, P. [1986] "The Devil's staircase," Physics Today, 38-45.
    • (1986) Physics Today , pp. 38-45
    • Bak, P.1
  • 3
    • 0000015344 scopus 로고    scopus 로고
    • Analytical and numerical studies of the Bonhoeffer van der Pol system
    • Barnes, B. & Grimshaw, R. [1997] "Analytical and numerical studies of the Bonhoeffer van der Pol system," J. Aust. Math. Soc. Series B, 38, 427-453.
    • (1997) J. Aust. Math. Soc. Series B , vol.38 , pp. 427-453
    • Barnes, B.1    Grimshaw, R.2
  • 5
    • 43949175578 scopus 로고
    • Critical dynamics of the Bonhoeffer van der Pol equation and its chaotic response to periodic stimulation
    • Braaksma, B. & Grasman, J. [1993] "Critical dynamics of the Bonhoeffer van der Pol equation and its chaotic response to periodic stimulation," Physica D68, 265-280.
    • (1993) Physica , vol.D68 , pp. 265-280
    • Braaksma, B.1    Grasman, J.2
  • 6
    • 4243304558 scopus 로고
    • Renormalisation, unstable manifolds, and the fractal structure of mode locking
    • Cvitanović, P., Jensen, M. H., Kadanoff, L. P. & Procaccia, I. [1985] "Renormalisation, unstable manifolds, and the fractal structure of mode locking," Phys. Rev. Lett. 55(4), 343-346.
    • (1985) Phys. Rev. Lett. , vol.55 , Issue.4 , pp. 343-346
    • Cvitanović, P.1    Jensen, M.H.2    Kadanoff, L.P.3    Procaccia, I.4
  • 7
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • Feigenbaum, M. [1978] "Quantitative universality for a class of nonlinear transformations," J. Stat. Phys. 19(1), 25-52.
    • (1978) J. Stat. Phys. , vol.19 , Issue.1 , pp. 25-52
    • Feigenbaum, M.1
  • 8
    • 0000450921 scopus 로고
    • Thresholds and plateaus in the Hodgkin-Huxley nerve equations
    • Fitzhugh, R. [1960] "Thresholds and plateaus in the Hodgkin-Huxley nerve equations," J. Gen. Physiol. 43, 867-895.
    • (1960) J. Gen. Physiol. , vol.43 , pp. 867-895
    • Fitzhugh, R.1
  • 9
    • 53349102813 scopus 로고
    • Impulses and physiological states in theoretical models of nerve membrane
    • Fitzhugh, R. [1961] "Impulses and physiological states in theoretical models of nerve membrane," Biophys. J. 1, 445-466.
    • (1961) Biophys. J. , vol.1 , pp. 445-466
    • Fitzhugh, R.1
  • 10
    • 1542356023 scopus 로고
    • Frequency entrainment of a forced van der Pol oscillator
    • Flaherty, J. E. & Hoppensteadt, F. C. [1978] "Frequency entrainment of a forced van der Pol oscillator," Studies Appl. Math. 58, 5-15.
    • (1978) Studies Appl. Math. , vol.58 , pp. 5-15
    • Flaherty, J.E.1    Hoppensteadt, F.C.2
  • 11
    • 0024036863 scopus 로고
    • Quasiperiodicity and dynamical systems: An experimentalist's view
    • Glazier, J. A. & Libchaber, A. [1988] "Quasiperiodicity and dynamical systems: An experimentalist's view," IEEE Trans. Circuits Syst. 35(7), 790-809.
    • (1988) IEEE Trans. Circuits Syst. , vol.35 , Issue.7 , pp. 790-809
    • Glazier, J.A.1    Libchaber, A.2
  • 12
    • 0012349493 scopus 로고
    • Crises, sudden changes in chaotic attractors and transient chaos
    • Grebogi, C., Ott, E. & Yorke, A. [1983] "Crises, sudden changes in chaotic attractors and transient chaos," Physica 7D, 181-200.
    • (1983) Physica , vol.7 D , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, A.3
  • 13
    • 0000498246 scopus 로고
    • Metamorphoses of basin boundaries in nonlinear dynamical systems
    • Grebogi, C., Ott, E. & Yorke, J. A. [1986] "Metamorphoses of basin boundaries in nonlinear dynamical systems," Phys. Rev. Lett. 56(10), 1011-1014.
    • (1986) Phys. Rev. Lett. , vol.56 , Issue.10 , pp. 1011-1014
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 15
    • 0001230012 scopus 로고
    • Intermittent chaos and low-frequency noise in the driven damped pendulum
    • Gwinn, E. G. & Westervelt, R. M. [1985] "Intermittent chaos and low-frequency noise in the driven damped pendulum," Phys. Rev. Lett. 54(15), 1613-1616.
    • (1985) Phys. Rev. Lett. , vol.54 , Issue.15 , pp. 1613-1616
    • Gwinn, E.G.1    Westervelt, R.M.2
  • 16
    • 4243798800 scopus 로고
    • Fractal basin boundaries and intermittency in the driven damped pendulum
    • Gwinn, E. G. & Westervelt, R. M. [1986] "Fractal basin boundaries and intermittency in the driven damped pendulum," Phys. Rev. A33(6), 4143-4155.
    • (1986) Phys. Rev. , vol.A33 , Issue.6 , pp. 4143-4155
    • Gwinn, E.G.1    Westervelt, R.M.2
  • 17
    • 0001029996 scopus 로고
    • Mode-locking and chaos in the Rayleigh-Bénard convection
    • Haucke, H. & Ecke, R. [1987] "Mode-locking and chaos in the Rayleigh-Bénard convection," Physica 25D, 307-329.
    • (1987) Physica , vol.25 D , pp. 307-329
    • Haucke, H.1    Ecke, R.2
  • 18
    • 0002135431 scopus 로고
    • Chaotic behavior in the Onchidium giant neuron under sinusoidal stimulation
    • Hayashi, H., Ishizuka, S., Ohta, M. & Hirakawa, K. [1982] "Chaotic behavior in the Onchidium giant neuron under sinusoidal stimulation," Phys. Lett. 88A(8), 435-438.
    • (1982) Phys. Lett. , vol.88 A , Issue.8 , pp. 435-438
    • Hayashi, H.1    Ishizuka, S.2    Ohta, M.3    Hirakawa, K.4
  • 19
    • 35649001607 scopus 로고
    • A quantitative description of membrane current and its application to conduction and excitation in nerve
    • Hodgkin, A. L. & Huxley, A. F. [1952] "A quantitative description of membrane current and its application to conduction and excitation in nerve," J. Physiol. 117, 500-544.
    • (1952) J. Physiol. , vol.117 , pp. 500-544
    • Hodgkin, A.L.1    Huxley, A.F.2
  • 20
    • 0001343758 scopus 로고
    • Complete devil's staircase, fractal dimension, and universality of mode-locking structure in the circle map
    • Jensen, M. H., Bak, P. & Bohr, T. [1983] "Complete devil's staircase, fractal dimension, and universality of mode-locking structure in the circle map," Phys. Rev. Lett. 50(21), 1637-1639.
    • (1983) Phys. Rev. Lett. , vol.50 , Issue.21 , pp. 1637-1639
    • Jensen, M.H.1    Bak, P.2    Bohr, T.3
  • 22
    • 0002417783 scopus 로고
    • Sudden change in the size of chaotic attractors: How does it occur?
    • eds. Kim, J. H. & Stringer, J. (John Wiley & Sons, New York)
    • Lai, Y., Grebogi, C. & Yorke, J. A. [1992] "Sudden change in the size of chaotic attractors: How does it occur?" in Applied Chaos, eds. Kim, J. H. & Stringer, J. (John Wiley & Sons, New York), pp. 441-455.
    • (1992) Applied Chaos , pp. 441-455
    • Lai, Y.1    Grebogi, C.2    Yorke, J.A.3
  • 23
    • 0002887375 scopus 로고
    • Qualitative analysis of the periodically forced relaxation oscillations
    • Levi, M. [1981] "Qualitative analysis of the periodically forced relaxation oscillations," Mem. Amer. Math. Soc. 32(244), 1-147.
    • (1981) Mem. Amer. Math. Soc. , vol.32 , Issue.244 , pp. 1-147
    • Levi, M.1
  • 24
    • 45949127771 scopus 로고
    • Different ways to turbulence in dissipative dynamical systems
    • Manneville, P. & Pomeau, Y. [1980] "Different ways to turbulence in dissipative dynamical systems," Physica 1D, 219-226.
    • (1980) Physica , vol.1 D , pp. 219-226
    • Manneville, P.1    Pomeau, Y.2
  • 25
    • 0004239863 scopus 로고
    • John Wiley & Sons, Chichester
    • Moon, F. C. [1987] Chaotic Vibrations (John Wiley & Sons, Chichester).
    • (1987) Chaotic Vibrations
    • Moon, F.C.1
  • 28
    • 34250254669 scopus 로고
    • Intermittent transition to turbulence in dissipative dynamical systems
    • Pomeau, Y. & Manneville, P. [1980] "Intermittent transition to turbulence in dissipative dynamical systems," Commun. Math. Phys. 74, 189-197.
    • (1980) Commun. Math. Phys. , vol.74 , pp. 189-197
    • Pomeau, Y.1    Manneville, P.2
  • 29
    • 0000748686 scopus 로고
    • Forced Bonhoeffer van der Pol oscillator in its excited mode
    • Rabinovitch, A., Thieberger, R. & Friedman, M. [1994] "Forced Bonhoeffer van der Pol oscillator in its excited mode," Phys. Rev. E50(2), 1574-1578.
    • (1994) Phys. Rev. , vol.E50 , Issue.2 , pp. 1574-1578
    • Rabinovitch, A.1    Thieberger, R.2    Friedman, M.3
  • 30
    • 0001248185 scopus 로고
    • Algorithms for controlling chaotic motion: Application for the BVP oscillator
    • Rajasekar, S. & Lakshmanan, M. [1993] "Algorithms for controlling chaotic motion: Application for the BVP oscillator," Physica D67, 282-300.
    • (1993) Physica , vol.D67 , pp. 282-300
    • Rajasekar, S.1    Lakshmanan, M.2
  • 31
    • 0001381681 scopus 로고
    • Period-doubling bifurcations, chaos, phase-locking and the devils staircase in a Bonhoeffer van der Pol oscillator
    • Rajasekar, S. & Lakshmanan, M. [1988] "Period-doubling bifurcations, chaos, phase-locking and the devils staircase in a Bonhoeffer van der Pol oscillator," Physica D32, 146-152.
    • (1988) Physica , vol.D32 , pp. 146-152
    • Rajasekar, S.1    Lakshmanan, M.2
  • 32
    • 0010900764 scopus 로고
    • Forecasting catastrophes by exploiting chaotic dynamics
    • ed. Kim, J. H. & Stringer, J. (John Wiley & Sons, New York)
    • Stewart, H. B. & Lansbury, A. N. [1992] "Forecasting catastrophes by exploiting chaotic dynamics," in Applied Chaos, ed. Kim, J. H. & Stringer, J. (John Wiley & Sons, New York), pp. 393-410.
    • (1992) Applied Chaos , pp. 393-410
    • Stewart, H.B.1    Lansbury, A.N.2
  • 33
    • 84974266266 scopus 로고
    • Numerical analysis of dynamical systems
    • Stuart, A. [1994] "Numerical analysis of dynamical systems," Acta Numerica, 467-572.
    • (1994) Acta Numerica , pp. 467-572
    • Stuart, A.1
  • 36
    • 0002579708 scopus 로고
    • Quantifying chaos with Lyapunov exponents
    • ed. Holden, A. V. (Manchester Univ. Press)
    • Wolf, A. [1984] "Quantifying chaos with Lyapunov exponents," in Nonlinear Sciences Theory Applied, ed. Holden, A. V. (Manchester Univ. Press) 273-290.
    • (1984) Nonlinear Sciences Theory Applied , pp. 273-290
    • Wolf, A.1
  • 37
    • 0042318026 scopus 로고
    • Bifurcations and chaos of the Bonhoeffer van der Pol model
    • Wang, W. [1989] "Bifurcations and chaos of the Bonhoeffer van der Pol model," J. Phys. A: Math. Gen. 22, L627-L632.
    • (1989) J. Phys. A: Math. Gen. , vol.22
    • Wang, W.1
  • 38
    • 0008494528 scopus 로고
    • Determining Lyapunov exponents from a time series
    • Wolf, A., Swift, J. B., Swinney, H. L. & Vestano, J. A. [1985] "Determining Lyapunov exponents from a time series," Physica 16D, 285-317.
    • (1985) Physica , vol.16 D , pp. 285-317
    • Wolf, A.1    Swift, J.B.2    Swinney, H.L.3    Vestano, J.A.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.