论文标题
一个消费者的Rosenzweig-Macarthur模型和两个资源的Rosenzweig-Macarthur模型中的振荡不稳定
Instability of oscillations in the Rosenzweig-MacArthur model of one consumer and two resources
论文作者
论文摘要
在Rosenzweig-Macarthur模型中，研究了两个资源的系统$ R_1 $，$ R_2 $和一个消费者$ C $，并具有Holling II型功能响应。资源消耗的费率$β_i$ i = 1,2 $与条件$β_1+β_2= 1 $相结合。动态切换是由$ c $的最大化引入的：$dβ_1/dt =（1/τ）dc/dβ_1$，其中特征时间$τ$很大但有限。参数的空间在数值上探索了两个资源并存。结果表明，出现在$β_I= 0.5 $的$ C $和相互同步的$ r_i $的振荡被以$β_I$ $更大或更小的稳定为不稳定。然后，将系统驱动到$β_1> 0.5 $和$ r_1 <r_2 $或相反的固定点之一。这种行为被解释为一旦选择了消费者，就无法更改首选资源。
The system of two resources $R_1$, $R_2$ and one consumer $C$ is investigated within the Rosenzweig-MacArthur model with Holling type II functional response. The rates $β_i$ of consumption of resources $i=1,2$ are coupled by the condition $β_1+β_2=1$. The dynamic switching is introduced by a maximization of $C$: $dβ_1/dt=(1/τ) dC/dβ_1$, where the characteristic time $τ$ is large but finite. The space of parameters where both resources coexist is explored numerically. The results indicate that oscillations of $C$ and mutually synchronized $R_i$ which appear at $β_i=0.5$ are destabilized for $β_i$ larger or smaller. Then, the system is driven to one of fixed points where either $β_1>0.5$ and $R_1<R_2$ or the opposite. This behaviour is explained as an inability of the consumer to change the preferred resource, once it is chosen.
