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<p>In this paper, we propose a 2D delayed Homographic Ricker map by introducing delay terms into the survival functions and small leak terms in the 2D Homographic Ricker population model. The delay term accounts for the maturity period of both prey and predator populations before reproduction. We investigate the persistence, boundedness, and invariance of the proposed model and prove the existence and uniqueness of a positive equilibrium point using the analytic theory of sequences. Additionally, we examine the global asymptotic stability of the positive equilibrium point with the help of local asymptotic stability and global attractivity. Finally, we identify conditions under which the delay model exhibits the Neimark–Sacker bifurcation and the theoretical results are demonstrated through numerical simulations.</p>

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Dynamics of 2D delayed Homographic Ricker map

  • 期刊论文

  • 发表日期：

    2025年1月16日

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  • Aishwaraya,
  • V. V. M. S. Chandramouli

摘要

In this paper, we propose a 2D delayed Homographic Ricker map by introducing delay terms into the survival functions and small leak terms in the 2D Homographic Ricker population model. The delay term accounts for the maturity period of both prey and predator populations before reproduction. We investigate the persistence, boundedness, and invariance of the proposed model and prove the existence and uniqueness of a positive equilibrium point using the analytic theory of sequences. Additionally, we examine the global asymptotic stability of the positive equilibrium point with the help of local asymptotic stability and global attractivity. Finally, we identify conditions under which the delay model exhibits the Neimark–Sacker bifurcation and the theoretical results are demonstrated through numerical simulations.