Asik Lale, Kulik Jackson, Long Kevin, Peace Angela
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USA.
Math Biosci Eng. 2018 Dec 19;16(1):501-515. doi: 10.3934/mbe.2019023.
Many population systems are subject to seasonally varying environments. As a result, many species exhibit seasonal changes in their life-history parameters. It is quite natural to try to understand how seasonal forcing affects population dynamics subject to stoichiometric constraints, such as nutrient/light availability and food quality. Here, we use a variation of a stoichiometric Lotka-Volterra type model, known as the LKE model, as a case study, focusing on seasonal variation in the producer's light-dependent carrying capacity. Positivity and boundedness of model solutions are studied, as well as numerical explorations and bifurcations analyses. In the absence of seasonal effects, the LKE model suggests that the dynamics are either stable equilibrium or limit cycles. However, through bifurcation analysis we observe that seasonal forcing can lead to complicated population dynamics, including periodic and quasi-periodic solutions.
许多种群系统都受到季节性变化的环境影响。因此，许多物种在其生活史参数上表现出季节性变化。尝试理解季节性强迫如何影响受化学计量约束（如养分/光照可用性和食物质量）的种群动态是很自然的。在这里，我们以一种化学计量的洛特卡-沃尔泰拉类型模型的变体（称为LKE模型）为例进行研究，重点关注生产者的光依赖承载能力的季节性变化。研究了模型解的正性和有界性，以及数值探索和分岔分析。在没有季节性影响的情况下，LKE模型表明动态要么是稳定平衡，要么是极限环。然而，通过分岔分析我们观察到季节性强迫会导致复杂的种群动态，包括周期和准周期解。
