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On Telegraph Reaction Diffusion And Coupled Map Lattice In Some Biological Systems

Author

Listed:
  • E. AHMED

    (Mathematics Department, Faculty of Sciences, Al-Ain P. O. Box 17551, U. A. E.;
    Mathematics Department, Faculty of Sciences, Mansura, 35516, Egypt)

  • H. A. ABDUSALAM

    (Mathematics Department, Faculty of Sciences, Cairo University, Giza, Egypt)

  • E. S. FAHMY

    (Mathematics Department, Faculty of Sciences, Cairo University, Giza, Egypt)

Abstract

It is argued that telegraph equation is more suitable than ordinary diffusion equation in modeling reaction diffusion in biological, economic and social systems. Telegraph reaction diffusion (TRD) is studied in one and two spatial dimensions. Some exact and approximate results are obtained. A coupled map lattice (CML) corresponding to the spatial prisoner's dilemma game is constructed and studied in the weak diffusion limit. A formula is derived for Lyapunov exponents and it is shown that periodic solutions are dense in the weak coupling regime and that this system is structurally stable.

Suggested Citation

  • E. Ahmed & H. A. Abdusalam & E. S. Fahmy, 2001. "On Telegraph Reaction Diffusion And Coupled Map Lattice In Some Biological Systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 717-726.
    • Handle: RePEc:wsi:ijmpcx:v:12:y:2001:i:05:n:s0129183101001936
    DOI: 10.1142/S0129183101001936
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    Cited by:

    1. Abdusalam, H.A., 2006. "Asymptotic solution of wave front of the telegraph model of dispersive variability," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1190-1197.
    2. Weam Alharbi & Sergei Petrovskii, 2018. "Critical Domain Problem for the Reaction–Telegraph Equation Model of Population Dynamics," Mathematics, MDPI, vol. 6(4), pages 1-15, April.
    3. Fei Ma & Fei Liu & Kum Fai Yuen & Polin Lai & Qipeng Sun & Xiaodan Li, 2019. "Cascading Failures and Vulnerability Evolution in Bus–Metro Complex Bilayer Networks under Rainstorm Weather Conditions," IJERPH, MDPI, vol. 16(3), pages 1-30, January.
    4. Abdusalam, H.A. & Fahmy, E.S., 2009. "Exact solution for the generalized Telegraph Fisher’s equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1550-1556.

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