Department of Mathematics, University of Kalyani, Kalyani 741235, Nadia, India.
Chaos. 2023 Feb;33(2):023106. doi: 10.1063/5.0122206.
In this article, we contemplate the dynamics of a three-tier system of nutrient, phytoplankton, and zooplankton with a gestation delay of discrete type and a distributed delay in nutrient recycling. Phytoplankton secretion-mediated alteration in the grazing pattern of zooplankton is encapsulated by a Monod-Haldane functional response. We carry out global sensitivity analysis for identifying the crucial model parameters having a significant impact on zooplankton density. The system potentially exhibits bistable configurations under identical ecological conditions by allowing different bifurcation scenarios, including multiple saddle-node and transcritical bifurcations with varying input rates of nutrients and inhibitory effects of phytoplankton against zooplankton. We observe that the gestation delay in zooplankton is responsible for the emergence of noxious bloom events. Interestingly, when the delay parameter crosses a threshold, the system experiences chaotic disorder, which prognosticates the onset of irregular bloom. Furthermore, by adding Gaussian white noise, we have extended the deterministic model to its stochastic counterpart. We found that white noise appears to regulate the survival and extinction of interacting populations. Comprehensive numerical simulations are consistent with mathematical results prognosticated by linear analysis.
本文探讨了一个具有离散型妊娠延迟和营养物质再循环分布延迟的三层营养、浮游植物和浮游动物系统的动态。浮游植物分泌介导的浮游动物摄食模式的改变由 Monod-Haldane 功能响应来描述。我们进行了全局敏感性分析，以确定对浮游动物密度有重大影响的关键模型参数。在相同的生态条件下，该系统通过允许不同的分岔情景，包括具有不同营养物质输入率和浮游植物对浮游动物抑制作用的多个鞍结分岔和超越分岔，表现出双稳态配置。我们观察到，浮游动物的妊娠延迟是产生有害水华事件的原因。有趣的是，当延迟参数超过一个阈值时，系统会经历混沌无序，预示着不规则水华的发生。此外，通过添加高斯白噪声，我们将确定性模型扩展到其随机模型。我们发现，白噪声似乎调节了相互作用种群的生存和灭绝。综合数值模拟与线性分析预测的数学结果一致。
