We study the interspecies competition in a simple resource–consumer model which includes the resource supply as a dynamic variable. In the model, an organism of each species needs to consume a certain minimum rate of resource (food) to survive; a higher rate of consumption is required for reproduction. We analyze the orbit diagrams and Lyapunov exponents in order to characterize the system dynamical behavior. We observe that under a periodic food supply, the system can exhibit coexistence in the form of limit cycle oscillations. For a certain parameter range, we observe chaotic behavior emerging from successive period doublings and quasi-periodicity.

中文翻译：

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资源-消费者模型中的混沌共存

我们在一个简单的资源消费者模型中研究种间竞争，该模型将资源供应作为一个动态变量。在模型中，每个物种的生物都需要消耗一定的最低资源（食物）率才能生存；再生产需要更高的消费率。我们分析轨道图和 Lyapunov 指数以表征系统的动态行为。我们观察到，在周期性的食物供应下，系统可以以极限循环振荡的形式表现出共存。对于一定的参数范围，我们观察到连续周期倍增和准周期出现的混沌行为。