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<p>This study investigates the dynamics of a dissolved oxygen–plankton system described by reaction-diffusion equations incorporating two discrete delays. Under certain conditions, the system admits three equilibria. Crossing curves are constructed on the two-delay plane to analyze the stability of the positive equilibrium and the existence of Hopf bifurcation. Moreover, the normal form on the center manifold near the Hopf bifurcation point is derived. Numerical simulations are carried out to verify the theoretical findings and reveal that a double Hopf bifurcation may emerge at the intersection of the bifurcation curves.</p>

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Bifurcation induced by dual delays in a diffusive dissolved oxygen–plankton system

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Zhichao Jiang,
  • Bohai Chen,
  • Yuezhen Wang

摘要

This study investigates the dynamics of a dissolved oxygen–plankton system described by reaction-diffusion equations incorporating two discrete delays. Under certain conditions, the system admits three equilibria. Crossing curves are constructed on the two-delay plane to analyze the stability of the positive equilibrium and the existence of Hopf bifurcation. Moreover, the normal form on the center manifold near the Hopf bifurcation point is derived. Numerical simulations are carried out to verify the theoretical findings and reveal that a double Hopf bifurcation may emerge at the intersection of the bifurcation curves.