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<p>Based on the promoting effect of cannibalistic behavior on the egg-laying rate of adult individuals, this study constructs a dual-delay predator-prey system incorporating stage structure and Holling-II functional response, with both behavioral response delay and gestation delay. The objective is to reveal the influence mechanism of multi-delay coupling on population dynamics and ecosystem stability. Firstly, under a no-delay condition, the positive invariant set of the system is established, and the existence and local asymptotic stability of the positive equilibrium point within this set are analyzed, laying the foundation for subsequent delayed system studies. Secondly, using the cannibalism rate as a bifurcation parameter, the triggering conditions and dynamic evolution of Hopf bifurcation in the delay-free system are explored. Thirdly, for the dual-delay system, the conditions for Hopf bifurcation induced by either or both types of delays are derived. By employing the center manifold theorem and normal form theory, the key parameters determining the nature of Hopf bifurcation are obtained. Finally, numerical simulations are conducted to verify the correctness of the theoretical results.</p>

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Stability and Hopf Bifurcation in Dual-Delay Cannibalistic Ecosystems with Stage Structure

  • 期刊论文

  • 发表日期：

    2026年5月20日

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  • Wangwang Liu,
  • Xiaolin Lin,
  • Danfeng Pang,
  • Yawei Xue

摘要

Based on the promoting effect of cannibalistic behavior on the egg-laying rate of adult individuals, this study constructs a dual-delay predator-prey system incorporating stage structure and Holling-II functional response, with both behavioral response delay and gestation delay. The objective is to reveal the influence mechanism of multi-delay coupling on population dynamics and ecosystem stability. Firstly, under a no-delay condition, the positive invariant set of the system is established, and the existence and local asymptotic stability of the positive equilibrium point within this set are analyzed, laying the foundation for subsequent delayed system studies. Secondly, using the cannibalism rate as a bifurcation parameter, the triggering conditions and dynamic evolution of Hopf bifurcation in the delay-free system are explored. Thirdly, for the dual-delay system, the conditions for Hopf bifurcation induced by either or both types of delays are derived. By employing the center manifold theorem and normal form theory, the key parameters determining the nature of Hopf bifurcation are obtained. Finally, numerical simulations are conducted to verify the correctness of the theoretical results.