一类种群策略调控下海洋营养-浮游植物-浮游动物Filippov模型的分岔与混沌

Bifurcation and Chaos in a Class of Population Strategy-regulated Marine Nutrient-phytoplankton-zooplankton Filippov Model

针对种群策略调控下浮游模型的稳定性以及多种分岔与混沌现象等问题,建立了一类与海洋生态系统相关的三维营养-浮游植物-浮游动物Filippov模型。利用非光滑动力系统的定性技术,研究了子系统和滑动向量场中平衡点的稳定性和分岔集,并得到了跨临界分岔、滑动分岔等丰富行为。最终证明控制阈值参数在0.1附近时发生了倍周期分叉乃至混沌。该研究可用于海洋生态保护等实际领域,有利于促进Filippov生态系统的动力学理论发展。

Aiming at the stability of the planktonic model under the regulation of population strategy and multiple bifurcation and chaos phenomena,a class of three-dimensional nutrient-phytoplankton-zooplankton Filippov models related to marine ecosystems was established.Qualitative techniques were used to investigate the stability of equilibria and bifurcation sets in subsystems and sliding vector fields,yielding enriched behaviors such as transcritical bifurcations and sliding bifurcations.It was finally demonstrated that the model experienced period doubling bifurcation and chaos when the threshold parameter was controlled around 0.1.This study could be applied to practical fields such as marine ecological protection,which could be conducive to the promotion of the dynamical theory of Filippov ecosystems.