Excitable population dynamics, biological control failure, and spatiotemporal pattern formation in a model ecosystem. (English) Zbl 1163.92040

Summary: Biological control has been attracting an increasing attention over the last two decades as an environmentally friendly alternative to the more traditional chemical-based control. We address robustness of the biological control strategy with respect to fluctuations in the controlling species density. Specifically, we consider a pest being kept under control by its predator. The predator response is assumed to be of Holling type III, which makes the system’s kinetics “excitable.” The system is studied by means of mathematical modeling and extensive numerical simulations.
We show that the system response to perturbations in the predator density can be completely different in spatial and non-spatial systems. In the nonspatial system, an overcritical perturbation of the population density results in a pest outbreak that will eventually decay with time, which can be regarded as a success of the biological control strategy. However, in the spatial system, a similar perturbation can drive the system into a self-sustained regime of spatiotemporal pattern formation with a high pest density, which is clearly a biological control failure. We then identify the parameter range where the biological control can still be successful and describe the corresponding regime of the system dynamics. Finally, we identify the main scenarios of the system response to the population density perturbations and reveal the corresponding structure of the parameter space of the system.


92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
93C95 Application models in control theory
65C20 Probabilistic models, generic numerical methods in probability and statistics
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