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Prog. Theor. Phys. Vol. 61 No. 1 (1979) pp. 45-53
Perturbation Theory of Self-Oscillating System with a Periodic Perturbation
Akira Itō
Department of Physics, Kyoto University, Kyoto 606
(Received August 11, 1978)
Abstract:
If a small periodic perturbation is applied to the self-oscillating system, it will, in some cases, entrain the system, in other cases, the system oscillates independently. These behaviours are examined numerically by Tomita et al. in a famous model chemical reaction–Brusselator. In this paper, a perturbation method is applied to obtain analytically the behaviour of the system under a periodic perturbational force. This method is applicable near the onset of the limit cycle oscillations.
URL :
http://ptp.ipap.jp/link?PTP/61/45/
DOI : 10.1143/PTP.61.45
References:
- P. Glansdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuations (Wiley, London, 1971).
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K. Tomita and T. Kai, Phys. Lett. A 66 (1978), 91[CrossRef]; Prog. Theor. Phys. 61 (1979), 54[PTP].
- Y. Kuramoto and T. Tsuzuki, Prog. Theor. Phys. 52 (1974), 1399[PTP].
- A. Itō, T. Ohta and H. Mashiyama, Prog. Theor. Phys. 54 (1975), 585[PTP].
- McLachlan, Theory and Application of Mathieu Functions (Oxford University Press, 1947).
Citing Article(s) :
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Progress of Theoretical Physics Vol. 61 No. 3 (1979) pp. 815-824
:
-
Successive Subharmonic Bifurcations and Chaos in a Nonlinear Mathieu Equation
-
Akira Itō
-
Progress of Theoretical Physics Vol. 62 No. 3 (1979) pp. 620-628
:
-
A Perturbation Theory of a Quasi-Periodic Motion
-
Akira Itō
-
Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1519-1532
:
-
Thermal Fluctuation of a Self-Oscillating Reaction System under a Periodic External Force. II
-
Hiroaki Daido and Kazuhisa Tomita
-
Progress of Theoretical Physics Vol. 66 No. 2 (1981) pp. 385-405
:
-
Control and Dissipation in Oscillatory Chemical Engines
-
Peter H. Richter, Paul Rehmus and John Ross
