In this paper, we analyze the complexity of an eco-epidemiological model for phytoplankton–zooplankton system in presence of toxicity and time delay. Holling type II function response is incorporated to address the predation rate as well as toxic substance distribution in zooplankton. It is also presumed that infected phytoplankton does recover from the viral infection. In the absence of time delay, stability and Hopf-bifurcation conditions are investigated to explore the system dynamics around all the possible equilibrium points. Further, in the presence of time delay, conditions for local stability are derived around the interior equilibria and the properties of the periodic solution are obtained by applying normal form theory and central manifold arguments. Computational simulation is performed to illustrate our theoretical findings. It is explored that system dynamics is very sensitive corresponding to carrying capacity and toxin liberation rate and able to generate chaos. Further, it is observed that time delay in the viral infection process can destabilize the phytoplankton density whereas zooplankton density remains in its old state. Incorporation of time delay also gives the scenario of double Hopf-bifurcation. Some control parameters are discussed to stabilize system dynamics. The effect of time delay on (i) growth rate of susceptible phytoplankton shows the extinction and double Hopf-bifurcation in the zooplankton population, (ii) a sufficiently large value of carrying capacity stabilizes the chaotic dynamics or makes the whole system chaotic with further increment.

在本文中，我们分析了存在毒性和时间延迟的浮游植物-浮游动物系统生态流行病学模型的复杂性。Holling II 型功能响应被纳入解决浮游动物的捕食率和有毒物质分布。还推测受感染的浮游植物确实从病毒感染中恢复。在没有时间延迟的情况下，研究了稳定性和 Hopf 分岔条件，以探索所有可能平衡点周围的系统动力学。此外，在存在时间延迟的情况下，围绕内部平衡推导了局部稳定性的条件，并通过应用范式理论和中心流形论证获得了周期解的性质。执行计算模拟以说明我们的理论发现。探索了系统动力学对承载能力和毒素释放率非常敏感并且能够产生混沌。此外，据观察，病毒感染过程中的时间延迟会使浮游植物密度不稳定，而浮游动物密度仍保持其旧状态。时间延迟的结合也给出了双 Hopf 分岔的场景。讨论了一些控制参数以稳定系统动态。时间延迟对 (i) 易感浮游植物生长速率的影响显示浮游动物种群的灭绝和双 Hopf 分叉，(ii) 足够大的承载能力值稳定混沌动力学或使整个系统随着进一步增加而混沌.