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Nonlinear dynamics and strange attractors in the biological system

Author

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  • Kadji, H.G. Enjieu
  • Orou, J.B. Chabi
  • Yamapi, R.
  • Woafo, P.

Abstract

This paper deals with the nonlinear dynamics of the biological system modeled by the multi-limit cycles Van der Pol oscillator. Both the autonomous and non-autonomous cases are considered using the analytical and numerical methods. In the autonomous state, the model displays phenomenon of birhythmicity while the harmonic oscillations with their corresponding stability boundaries are tackled in the non-autonomous case. Conditions under which superharmonic, subharmonic and chaotic oscillations occur in the model are also investigated. The analytical results are validated and supplemented by the results of numerical simulations.

Suggested Citation

  • Kadji, H.G. Enjieu & Orou, J.B. Chabi & Yamapi, R. & Woafo, P., 2007. "Nonlinear dynamics and strange attractors in the biological system," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 862-882.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:862-882
    DOI: 10.1016/j.chaos.2005.11.063
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    References listed on IDEAS

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    1. Chi-Sang Poon & Christopher K. Merrill, 1997. "Decrease of cardiac chaos in congestive heart failure," Nature, Nature, vol. 389(6650), pages 492-495, October.
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    Cited by:

    1. Yonkeu, R. Mbakob, 2023. "Stochastic bifurcations induced by Lévy noise in a fractional trirhythmic van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    2. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Járdánházy, Anett & Molnár, Márk & Járdánházy, Tamás, 2009. "Point correlation dimension can reveal functional changes caused by gap junction blockers in the 4-aminopyridine in vivo rat epilepsy model," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 286-297.
    4. Fu, Peng & Wang, Can-Jun & Yang, Ke-Li & Li, Xu-Bo & Yu, Biao, 2022. "Reentrance-like vibrational resonance in a fractional-order birhythmic biological system," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    5. Nganso, E. Njinkeu & Mbouna, S.G. Ngueuteu & Yamapi, R. & Filatrella, G. & Kurths, J., 2023. "Two-attractor chimera and solitary states in a network of nonlocally coupled birhythmic van der Pol oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    6. Mbakob Yonkeu, R. & David, Afungchui, 2022. "Coherence and stochastic resonance in the fractional-birhythmic self-sustained system subjected to fractional time-delay feedback and Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).

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