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Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model
Author(s) -
Singh Anuraj,
Elsadany Abdelalim A.,
Elsonbaty Amr
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5628
Subject(s) - mathematics , discretization , bifurcation , chaotic , stability (learning theory) , bounded function , complex dynamics , statistical physics , stability theory , control theory (sociology) , mathematical analysis , nonlinear system , physics , computer science , quantum mechanics , artificial intelligence , machine learning , control (management)
A proposed discretized form of fractional‐order prey‐predator model is investigated. A sufficient condition for the solution of the discrete system to exist and to be unique is determined. Jury stability test is applied for studying stability of equilibrium points of the discretized system. Then, the effects of varying fractional order and other parameters of the systems on its dynamics are examined. The system undergoes Neimark‐Sacker and flip bifurcation under certain conditions. We observe that the model exhibits chaotic dynamics following stable states as the memory parameter α decreases and step size h increases. Theoretical results illustrate the rich dynamics and complexity of the model. Numerical simulation validates theoretical results and demonstrates the presence of rich dynamical behaviors include S‐asymptotically bounded periodic orbits, quasi‐periodicity, and chaos. The system exhibits a wide range of dynamical behaviors for fractional‐order α key parameter.