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Complex oscillatory behaviour in a delayed protein cross talk model with periodic forcing

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  • Nikolov, Svetoslav

Abstract

The purpose of this paper is to examine the effects of periodic forcing on the time delay protein cross talk model behaviour. We assume periodic variation for the plasma membrane permeability. The dynamic behaviour of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing can very easily give rise to complex dynamics, including a period-doubling cascade, chaos, quasi-periodic oscillating, and periodic windows. Finally, we calculate the maximal Lyapunov exponent in the regions of the parameter space where chaotic motion of delayed protein cross talk model with periodic forcing exists.

Suggested Citation

  • Nikolov, Svetoslav, 2009. "Complex oscillatory behaviour in a delayed protein cross talk model with periodic forcing," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 385-395.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:385-395
    DOI: 10.1016/j.chaos.2008.12.007
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    References listed on IDEAS

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    1. Wu, Xiaoqun & Lu, Jun-an & Iu, Herbert H.C. & Wong, Siu-Chung, 2007. "Suppression and generation of chaos for a three-dimensional autonomous system using parametric perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 31(4), pages 811-819.
    2. Mihalaş, Gh.I. & Neamţu, M. & Opriş, D. & Horhat, R.F., 2006. "A dynamic P53-MDM2 model with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 936-945.
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