Abstract
This paper is concerned with the existence and stability of steady state solutions for the SKT biological competition model with cross-diffusion.
By applying the detailed spectral analysis and in virtue of the bifurcating direction to the limiting system as the cross diffusion rate tends to infinity, it is proved the stability/instability of the nontrivial positive steady states with some special bifurcating structure.
Further, the existence and stability/instability of the corresponding nontrivial positive steady states for the original cross-diffusion system are proved by applying perturbation argument.
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This paper is supported by the National Natural Science Foundation of China (No. 11871048, No. 11501031, No.11471221, No.11501016),Premium Funding Project for Academic Human Resources Development in Beijing Union University(BPHR2019CZ07, BPHR2020EZ01) and Beijing Municipal Education Commission (KZ201310028030,KM202011417010).
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Li, Q., Xu, Q. The Stability of Nontrivial Positive Steady States for the SKT Model with Large Cross Diffusion. Acta Math. Appl. Sin. Engl. Ser. 36, 657–669 (2020). https://doi.org/10.1007/s10255-020-0951-2
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DOI: https://doi.org/10.1007/s10255-020-0951-2