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Prog. Theor. Phys. Vol. 68 No. 5 (1982) pp. 1543-1560

[ Full Text PDF : FREE ACCESS (671K) ]

Some Routes to Chaos from Limit Cycle in the Forced Lorenz System

Tatsuya Uezu and Yoji Aizawa

Department of Physics, University of Kyoto, Kyoto 606

(Received June 7, 1982)

Abstract:

Previously we have investigated the response of the Lorenz system under periodic perturbation. In this paper, we focus on the transition from a limit cycle to chaos in the same system. The following three cases of the transition are studied:
(I) Chaos through cascades of subharmonic bifurcation.In the periodic region, the stroboscopic mapping in the system is approximated by the Hénon mapping. We obtain the Feigenbaum constant δ=4.715.
(II) Chaos due to the production of a homoclinic intersection in the stroboscopic picture. The system shows Intermittency.
(III) Chaos due to the production of a pair of heteroclinic intersections in the stroboscopic picture.The system shows Intermittency. The resultant strange attractor has a positive two-dimensional Lyapunov characteristic number.
Power spectra and Lyapunov characteristic numbers are obtained numerically in each case.Furthermore, in connection with Case (II), we show that in a system which has a certain type of spatial symmetry such as is found in the Lorenz model, a symmetric solution cannot undergo subharmonic bifurcation.


URL : http://ptp.ipap.jp/link?PTP/68/1543/
DOI : 10.1143/PTP.68.1543

[ Full Text PDF : FREE ACCESS (671K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 1864-1879 :
    Global Aspects of the Dissipative Dynamical Systems. II
    Yoji Aizawa and Tatsuya Uezu
  2. Progress of Theoretical Physics Vol. 70 No. 3 (1983) pp. 879-882 :
    Resonance and Intermittent Transition from Torus to Chaos in Periodically Forced Systems near Intermittency Threshold
    Hiroaki Daido
  3. Progress of Theoretical Physics Vol. 83 No. 5 (1990) pp. 850-874 :
    Topological Structure in Flow Systems
    Tatsuya Uezu
  4. Progress of Theoretical Physics Vol. 112 No. 5 (2004) pp. 785-796 :
    Global Dynamics in the Periodically Forced Chen System
    Debin Huang
  5. Progress of Theoretical Physics Supplement No.79 (1984) pp. 75-95 :
    Coupling Sensitivity of Chaos
    Hiroaki Daido

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