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Complex Dynamics and Bifurcations Analysis of Discrete-Time Modified Leslie–Gower System

Author

Listed:
  • Anuraj Singh

    (ABV-Indian Institute of Information Technology and Management Gwalior, India)

  • Ankit Parwaliya

    (ABV-Indian Institute of Information Technology and Management Gwalior, India)

  • Ajay Kumar

    (ABV-Indian Institute of Information Technology and Management Gwalior, India)

  • Amr Elsonbaty

    (��Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia§Department of Engineering Mathematics and Physics, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt)

  • A. A. Elsadany

    (��Department of Mathematics, College of Sciences and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia¶Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia 41522, Egypt)

Abstract

This work introduces a discrete modified Leslie–Gower prey–predator system with Holling type-II functional response. The persistence of the discrete model under certain conditions is discussed. The conditions assuring the existence of fixed points are derived and nonlinear dynamics of system are explored at these fixed points. It has been shown that the system exhibits transcritical bifurcation and flip bifurcation at semi-trivial fixed point under certain bifurcation values. In addition, the center manifold and bifurcation theories are employed to attain the conditions for existence of flip and Neimark–Sacker bifurcations at coexistence fixed point. The system is found to exhibit periodic solutions along with bifurcations leading to wide range of chaotic dynamics. The numerical simulations are performed to confirm the analytical analysis.

Suggested Citation

  • Anuraj Singh & Ankit Parwaliya & Ajay Kumar & Amr Elsonbaty & A. A. Elsadany, 2024. "Complex Dynamics and Bifurcations Analysis of Discrete-Time Modified Leslie–Gower System," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 857-882, November.
    • Handle: RePEc:wsi:nmncxx:v:20:y:2024:i:03:n:s1793005724500455
    DOI: 10.1142/S1793005724500455
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