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Modeling of invasion on a heterogeneous habitat: taxis and multistability

Author

Listed:
  • Frischmuth, Kurt
  • Budyansky, Alexander V.
  • Tsybulin, Vyacheslav G.

Abstract

We study a mathematical model of invasion in the case of two closely related species. The model is formulated as a system of nonlinear partial differential equations, which takes into account the diffusion and taxis of both species as well as their competition for a heterogeneous resource (carrying capacity). We derive analytical and numerical techniques based on the cosymmetry approach. Parameter relations are established for which the given model admits a continuous family of stationary distributions. This implies multistability, i.e. the existence of successful invasion scenarios with different final states. Then, we treat the general situation as a disturbance of this cosymmetric case and develop methods for forecasting. Numerical results of the one-dimensional spatial problem demonstrate the effectiveness of the chosen methodology. In particular, we show the possibility to predict, by accurate long-term calculations, final states in the case of slow evolution. Further, we are able to classify taxis parameters with respect to success or failure of an invasion.

Suggested Citation

  • Frischmuth, Kurt & Budyansky, Alexander V. & Tsybulin, Vyacheslav G., 2021. "Modeling of invasion on a heterogeneous habitat: taxis and multistability," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    • Handle: RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005452
    DOI: 10.1016/j.amc.2021.126456
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