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arXiv · 2205.11910

Instability of oscillations in the Rosenzweig-MacArthur model of one consumer and two resources

Przemysław Gawroński·Alfio Borzì·Krzysztof Kułakowski
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Abstract

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 $\beta_i$ of consumption of resources $i=1,2$ are coupled by the condition $\beta_1+\beta_2=1$. The dynamic switching is introduced by a maximization of $C$: $d\beta_1/dt=(1/\tau) dC/d\beta_1$, where the characteristic time $\tau$ 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 $\beta_i=0.5$ are destabilized for $\beta_i$ larger or smaller. Then, the system is driven to one of fixed points where either $\beta_1>0.5$ 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.

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Przemysław Gawroński, Alfio Borzì, Krzysztof Kułakowski. 2022-05-24. Instability of oscillations in the Rosenzweig-MacArthur model of one consumer and two resources. https://doi.org/10.1063/5.0105340

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