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<p>This study discusses a mathematical model of a prey-predator system by using Ivlev-like nonmonotonic and Beddington–DeAngelis functional response. In this article, prey is endowed with defense capabilities. In the Non-spatial model, we have found boundedness, and stability (local and global) of the system. The Routh–Hurwitz condition is used to derive stability conditions. Hopf bifurcation is discussed with carrying capacity K. The normal theory is used to examine the Hopf bifurcation direction and the stability of bifurcating solutions. Moreover, the center manifold theorem has been determined to find non-hyperbolic equilibrium points stability. Moreover, the Hopf bifurcation along with direction and periodic solutions stability are performed. Chaotic behavior is observed with the change in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\beta \)</EquationSource> </InlineEquation>. We consider the chaotic dynamics and it is found that the system has chaotic dynamics. Furthermore, we also explored Hopf bifurcation and Turing instability of spatial model systems. This study demonstrates that group defense mechanism, in a balanced environment.</p>

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A Food Web Exhibiting Group Defenses in Spatiotemporal Dynamics

  • 期刊论文

  • 发表日期：

    2025年8月20日

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  • Surabhi Pareek,
  • Randhir Singh Baghel

摘要

This study discusses a mathematical model of a prey-predator system by using Ivlev-like nonmonotonic and Beddington–DeAngelis functional response. In this article, prey is endowed with defense capabilities. In the Non-spatial model, we have found boundedness, and stability (local and global) of the system. The Routh–Hurwitz condition is used to derive stability conditions. Hopf bifurcation is discussed with carrying capacity K. The normal theory is used to examine the Hopf bifurcation direction and the stability of bifurcating solutions. Moreover, the center manifold theorem has been determined to find non-hyperbolic equilibrium points stability. Moreover, the Hopf bifurcation along with direction and periodic solutions stability are performed. Chaotic behavior is observed with the change in \(\beta \) . We consider the chaotic dynamics and it is found that the system has chaotic dynamics. Furthermore, we also explored Hopf bifurcation and Turing instability of spatial model systems. This study demonstrates that group defense mechanism, in a balanced environment.