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Bifurcation and chaos in a discrete physiological control system

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  • Li, Li

Abstract

In this paper, we introduce a new method to discrete a physiological control system with delay and investigate the dynamical behavior of the discrete model. Basic properties of the discrete system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagrams. Analysis results show that this system has complex dynamics with some interesting characteristics which may provide some new knowledge for us in fields of physiology.

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  • Li, Li, 2015. "Bifurcation and chaos in a discrete physiological control system," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 397-404.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:397-404
    DOI: 10.1016/j.amc.2014.11.107
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    1. Willox, R. & Grammaticos, B. & Carstea, A.S. & Ramani, A., 2003. "Epidemic dynamics: discrete-time and cellular automaton models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 13-22.
    2. Ramani, A. & Carstea, A.S. & Willox, R. & Grammaticos, B., 2004. "Oscillating epidemics: a discrete-time model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 333(C), pages 278-292.
    3. Kari Alitalo & Tuomas Tammela & Tatiana V. Petrova, 2005. "Lymphangiogenesis in development and human disease," Nature, Nature, vol. 438(7070), pages 946-953, December.
    4. Wang, Zhigang & Zhang, Haifeng & Wang, Zhen, 2014. "Multiple effects of self-protection on the spreading of epidemics," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 1-7.
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