Math. Model. Nat. Phenom.
Volume 11, Number 5, 2016Bifurcations and Pattern Formation in Biological Applications
|Page(s)||137 - 157|
|Published online||07 December 2016|
Fighting Enemies and Noise: Competition of Residents and Invaders in a Stochastically Fluctuating Environment
Systems Biology Laboratory, Melbourne School of Engineering The University of Melbourne, Parkville
2 Centre for Systems Genomics, University of Melbourne, Australia
3 Felix Bernstein Institute for Mathematical Statistics, Georg August University of Göttingen, Germany
4 Institute of Environmental Systems Research, School of Mathematics / Computer Science, Osnabrück University, Barbarastr. 12, 49076 Osnabrück, Germany
* Corresponding author. E-mail: firstname.lastname@example.org
The possible control of competitive invasion by infection of the invader and multiplicative noise is studied. The basic model is the Lotka-Volterra competition system with emergent carrying capacities. Several stationary solutions of the non-infected and infected system are identified as well as parameter ranges of bistability. The latter are used for the numerical study of invasion phenomena. The diffusivities, the infection but in particular the white and coloured multiplicative noise are the control parameters. It is shown that not only competition, possible infection and mobilities are important drivers of the invasive dynamics but also the noise and especially its color and the functional response of populations to the emergence of noise.
Mathematics Subject Classification: 35K57 / 35Q92 / 60H15
Key words: eco-epidemiological model / explicit and emergent carrying capacities / bioinvasion / resident–invader competition / biocontrol. infection / standard incidence / diffusion / multiplicative noise / coloured noise / functional response to noise
© EDP Sciences, 2016
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