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Chaotic behaviour in the Josephson equations with periodic force

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Abstract

The goal of this paper is to prove analytically the existence of chaos, for certain parameter values, in the dynamics of the Josephson equations

$$\dot \varphi = Y,\dot Y = - (\sin \varphi + k\sin 2\varphi ) - A(\cos \varphi + 2k\cos 2\varphi )Y + \beta + B\sin \omega t.$$
((E))

and

$$ \dot \varphi = Y,\dot Y = - (\sin \varphi + k\sin 2\varphi ) - aY + \beta + B\sin \omega t.$$
((F))

Combining our previous results with the new results, we obtain a more complete description of the dynamics of the Josephson equations.

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References

  1. Zhu-jun Jing, Application of Qualitative Methods of Differential Equations to Study Phase-Locked Loops,SIAM. J. Appl. Math. 43: 2 (1983), 1247–1258.

    Article  Google Scholar 

  2. Zhu-jun Jing, Study and Numerical Calculation of Separatrix Loop of Differential Equations in Phase-Locked Loop,Math. Practice Theory,4 (1980), 30–37.

    Google Scholar 

  3. Ji-bin Li and Zeng-Rong Lin, Chaotic Propertys for Several Non-Linear Forcing Oscillatory Systems,Acta. Math. Phys.,5: 2 (1985), 195–204.

    Google Scholar 

  4. Zhang Jin-yan and Qian Min, “Dynamical System and Its Applications” to Be Published by Peking University Press, 1988.

  5. J. Guckenheimer and P. J. holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, 1983.

  6. V. K. Melnikov, On The Stability of The Center for Time Periodic Perturbations,Trans. Moscow. Math. Soc.,12 (1963), 1–57.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Academia Sinica, China

    Jing Zhujun

  2. The Affiliated Middle School of Bejing University, China

    Wang Pengyuan

Authors
  1. Jing Zhujun
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  2. Wang Pengyuan
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Jing, Z., Wang, P. Chaotic behaviour in the Josephson equations with periodic force. Acta Mathematicae Applicatae Sinica 4, 289–295 (1988). https://doi.org/10.1007/BF02007232

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  • DOI: https://doi.org/10.1007/BF02007232

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