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Complex dynamic behavior in a food web consisting of two preys and a predator

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  • Gakkhar, Sunita
  • Singh, Brahampal

Abstract

This paper deals with the dynamic behavior of a realistic two preys and one predator system. The predator dynamics is governed by modified Leslie Gower model. The local and global stability analysis has been carried out. Conditions for stability of planar equilibrium points and positive equilibrium points have been obtained. Numerical simulations are carried out for biologically feasible choices of parameters to display the existence of non-chaotic and quasi-periodic solution of non-linear system.

Suggested Citation

  • Gakkhar, Sunita & Singh, Brahampal, 2005. "Complex dynamic behavior in a food web consisting of two preys and a predator," Chaos, Solitons & Fractals, Elsevier, vol. 24(3), pages 789-801.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:3:p:789-801
    DOI: 10.1016/j.chaos.2004.09.095
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    Cited by:

    1. Quansah, Emmanuel & Parshad, Rana D. & Mondal, Sumona, 2017. "Cold induced mortality of the Burmese Python: An explanation via stochastic analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 356-364.
    2. Chu, Yan-Dong & Chang, Ying-Xiang & Zhang, Jian-Gang & Li, Xian-Feng & An, Xin-Lei, 2009. "Full state hybrid projective synchronization in hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1502-1510.
    3. An, Xin-Lei & Yu, Jian-Ning & Chu, Yan-Dong & Zhang, Jian-Gang & Zhang, Li, 2009. "Global chaos synchronization of three coupled nonlinear autonomous systems and a novel method of chaos encryption," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 865-873.
    4. Parshad, Rana D. & Takyi, Eric M. & Kouachi, Said, 2019. "A remark on “Study of a Leslie-Gower predator-prey model with prey defense and mutual interference of predators” [Chaos, Solitons & Fractals 120 (2019) 1–16]," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 201-205.
    5. Zhang, Jian-Gang & Li, Xian-Feng & Chu, Yan-Dong & Yu, Jian-Ning & Chang, Ying-Xiang, 2009. "Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2150-2168.
    6. Gakkhar, Sunita & Singh, Brahampal, 2006. "Dynamics of modified Leslie–Gower-type prey–predator model with seasonally varying parameters," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1239-1255.
    7. Parshad, Rana D. & Kumari, Nitu & Kouachi, Said, 2015. "A remark on “Study of a Leslie–Gower-type tritrophic population model” [Chaos, Solitons and Fractals 14 (2002) 1275–1293]," Chaos, Solitons & Fractals, Elsevier, vol. 71(C), pages 22-28.
    8. Yang, Xiaofeng & Jin, Zhen & Xue, Yakui, 2007. "Weak average persistence and extinction of a predator–prey system in a polluted environment with impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 726-735.

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