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Homoclinic bifurcation in Chua’s circuit

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Abstract

We report our experimental observations of the Shil’nikov-type homoclinic chaos in asymmetry-induced Chua’s oscillator. The asymmetry plays a crucial role in the related homoclinic bifurcations. The asymmetry is introduced in the circuit by forcing a DC voltage. For a selected asymmetry, when a system parameter is controlled, we observed transition from large amplitude limit cycle to homoclinic chaos via a sequence of periodic mixed-mode oscillations interspersed by chaotic states. Moreover, we observed two intermediate bursting regimes. Experimental evidences of homoclinic chaos are verified with PSPICE simulations.

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References

  1. S Wiggins,Introduction to applied nonlinear dynamical systems and chaos (Springer-Verlag, NY, 1990)

    MATH  Google Scholar 

  2. Y A Kuznetsov,Elements of applied bifurcation theory (Springer-Verlag, NY, 1995)

    MATH  Google Scholar 

  3. V Petrov, S K Scott and K Showalter,J. Chem. Phys. 97, 6191 (1992)

    Article  ADS  Google Scholar 

  4. T Peacock and T Mullin,J. Fluid. Mech. 432, 369 (2001)

    MATH  ADS  Google Scholar 

  5. A N Pisarchik, R Meucci and F T Arecchi,Eur. Phys. J. D13, 385 (2001)

    ADS  Google Scholar 

  6. E Allaria, F T Arecchi, A Di Garbo and M Meucci,Phys. Rev. Lett. 86, 791 (2001)

    Article  ADS  Google Scholar 

  7. R Herrero, R Pons, J Farjas, F Pi and G Orriols,Phys. Rev. E53, 5627 (1996)

    ADS  Google Scholar 

  8. J J Healy, D S Broomhead, K A Cliffe, R Jones and T Mullin,Physica D48, 322 (1991)

    ADS  Google Scholar 

  9. R R Llinás,Science 243, 1654 (1988)

    Article  ADS  Google Scholar 

  10. M Breakspear, J R Terry and K J Friston,Network: Computation in Neural Computing 14, 703 (2003)

    Article  ADS  Google Scholar 

  11. V N Belykh, I V Belykh, M Colding-Jorgensen and E Mosekilde,Eur. Phys. J. E3, 205 (2000)

    Google Scholar 

  12. A L Shilnikov and N F Rulkov,Int. J. Bifurcat. Chaos 13, 3325 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  13. E M Izhikevich,Int. J. Bifurcat. Chaos 10, 1171 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  14. I P Marino, E Allaria, R Meucci, S Boccaletti and F T Arecchi,Chaos 13, 286 (2003)

    Article  ADS  Google Scholar 

  15. P Glendinning and C Sparrow,J. Stat. Phys. 135, 645 (1984)

    Article  MathSciNet  Google Scholar 

  16. P Gaspard and X-J Wang,J. Stat. Phys. 48, 151 (1987)

    Article  MathSciNet  Google Scholar 

  17. Marc T M Koper,Physica D80, 72 (1995)

    ADS  MathSciNet  Google Scholar 

  18. A Goryachev, P Strizhak and R Kapral,J. Chem. Phys. 107, 2881 (1997)

    Article  ADS  Google Scholar 

  19. S Rajesh and G Ananthakrishna,Physica D140, 193 (2000)

    ADS  Google Scholar 

  20. P Glendinning, J Abshagen and T Mullin,Phys. Rev. E64, 036208 (2001)

    ADS  Google Scholar 

  21. L O Chua, M Komuro and T Matsumoto,IEEE Trans. Cir. Systs. CAS-33, 1072 (1986)

    Article  ADS  MathSciNet  Google Scholar 

  22. M P Kennedy,IEEE Trans. Cir. Systs. CAS-40, 657 (1993)

    Article  Google Scholar 

  23. S K Dana and S Chakraborty,Int. J. Bifurcat. Chaos 14, 1375 (2004)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Material Research Centre and Centre for Condensed Matter Physics, Indian Institute of Science, 560 016, Bangalore, India

    G. Ananthakrishna

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  1. S. K. Dana
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  2. S. Chakraborty
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  3. G. Ananthakrishna
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Dana, S.K., Chakraborty, S. & Ananthakrishna, G. Homoclinic bifurcation in Chua’s circuit. Pramana - J Phys 64, 443–454 (2005). https://doi.org/10.1007/BF02704570

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