Multiple patterns formation for an aggregation/diffusion predator-prey system
نویسندگان
چکیده
<p style='text-indent:20px;'>We investigate existence of stationary solutions to an aggregation/diffusion system PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually proportional negative constant <inline-formula><tex-math id="M1">\begin{document}$ -\alpha $\end{document}</tex-math></inline-formula>, with id="M2">\begin{document}$ \alpha&gt;0 $\end{document}</tex-math></inline-formula>. Each also subject self-attraction forces together quadratic diffusion effects. The competition between aforementioned mechanisms produce rich asymptotic behavior, namely formation steady states composed multiple bumps, i.e. sums Barenblatt-type profiles. such states, under some conditions on positions bumps and proportionality id="M3">\begin{document}$ \alpha showed for small diffusion, using functional version Implicit Function Theorem. We complement our results numerical simulations, suggest large variety in possible strategies use order interact each other.</p>
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Article history: Received 3 November 2010 Revised 4 March 2011 Available online 24 March 2011 MSC: 35K57 35B36 35B32 92D40
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ژورنال
عنوان ژورنال: Networks and Heterogeneous Media
سال: 2021
ISSN: ['1556-1801', '1556-181X']
DOI: https://doi.org/10.3934/nhm.2021010