 Modeling of invasion on a heterogeneous habitat: taxis and multistabilityKurt Frischmuth, Alexander V. Budyansky and Vyacheslav G. Tsybulin Applied Mathematics and Computation, 2021, vol. 410, issue C 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. Keywords: Invasion; Competition; Diffusion; Taxis; Cosymmetry; Mulistability; Nonlinear PDEs (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:410:y:2021:i:c:s0096300321005452 DOI: 10.1016/j.amc.2021.126456 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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