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<p>This article presents a three-dimensional discrete-time ecological model to elucidate the intricate dynamics among three distinct species within an ecosystem. This approach extends traditional two-dimensional models, offering a more comprehensive perspective on ecological interactions. We identify all biologically feasible equilibria and perform a local stability analysis for each equilibrium point. Through bifurcation analysis (Neimark-Sacker and period-doubling bifurcations), we successfully demonstrate chaotic attractors via period doubling in the discrete-time model and implement chaos control through numerical simulations. By integrating this mathematical model, we derive ecological insights that contribute to informed conservation and management strategies, promoting sustainable biodiversity preservation.</p>

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Exploring Neimark-Sacker Bifurcation and Chaos Control in a Tri-species Discrete-Time Model

  • 期刊论文

  • 发表日期：

    2025年2月18日

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  • Sujay Goldar,
  • Sk. Sarif Hassan,
  • Krishna Pada Das,
  • Ahmed A. Mohsen,
  • Dahlia Khaled Bahlool,
  • Qasem Al-Mdallal,
  • Sourav Rana,
  • Vikas Gupta,
  • Purnendu Sardar

摘要

This article presents a three-dimensional discrete-time ecological model to elucidate the intricate dynamics among three distinct species within an ecosystem. This approach extends traditional two-dimensional models, offering a more comprehensive perspective on ecological interactions. We identify all biologically feasible equilibria and perform a local stability analysis for each equilibrium point. Through bifurcation analysis (Neimark-Sacker and period-doubling bifurcations), we successfully demonstrate chaotic attractors via period doubling in the discrete-time model and implement chaos control through numerical simulations. By integrating this mathematical model, we derive ecological insights that contribute to informed conservation and management strategies, promoting sustainable biodiversity preservation.