论文标题
竞争模型中表演的动态
Dynamics of Performances in a Competitive Model
论文作者
论文摘要
基于竞争性的Lotka-Volterra模型的集成模型和猎物前进的Rosenzweig-Macarthur模型，分析了一个竞争性资源消费者动力学模型，我们在本文中称其为LV-RM模型。资源的增长在没有消费者的情况下是逻辑，而竞争的消费者II型Holling的功能响应使模型结构更加现实。我们使用正常形式和中心歧管定理来对所提出的模型进行分叉分析，确定了Hopf和零HOPF分叉及其方向，并讨论了它们的生物学解释。我们假设，竞争消费者掠夺性的差异时间尺度导致竞争不对称的是通过放松振荡动力学促进共存的机制。但是，两个竞争对手的其他性能参数都是相同的。竞争系数相互作用后，第一个Lyapunov系数变化的图形表示显示了各种动力学，从周期状态到混沌运动等复杂性越来越复杂，如Rössler吸引子。我们提出了模拟，以可视化通过分叉分析获得的理论结果。
A competitive resource-consumer dynamical model is analyzed based on an integrated model of a competitive Lotka-Volterra model and a prey-predator Rosenzweig-MacArthur model that we call that LV-RM model throughout this paper. Resource growth in the absence of consumers is logistic, and competing consumers' type II Holling's functional response made the model structure more realistic. We used the normal form and the center manifold theorems for bifurcation analysis of the presented model, identified Hopf and zero-Hopf bifurcations and their directions, and discussed their biological interpretations. We hypothesized that differentiated time scales of the competing consumers' predatory that lead to asymmetry in competition are the mechanisms that promote coexistence through relaxation-oscillation dynamics. Though, other performance parameters of both competitors are the same. Graphical representation of variations of the first Lyapunov coefficient, after competition coefficients interplay, shows various dynamics with growing complexity from the periodic state towards chaotic motion like Rössler attractor. We presented simulations to visualize the theoretical results obtained through bifurcation analysis.
