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Existence and stability of traveling wavefronts for discrete three species competitive-cooperative systems

1 Department of Mathematics, National Central University, Chungli 32001, Taiwan
2 General Education Center, National Taipei University of Technology, Taipei 10608, Taiwan
3 School of Mathematics and Statistics, Xidian University, Xi’an, Shaanxi, 710071, P.R. China

Special Issues: Spatial dynamics for epidemic models with dispersal of organisms and heterogenity of environment

The purpose of this work is to investigate the existence and stability of traveling wavefronts for competitive-cooperative systems with three species. The existence result can be derived by using the technique of monotone method with the help of a pair of explicit supersolution and subsolution. Moreover, some su cient conditions ensure the linear determinacy for the minimal speed is given. Then, applying the weighted energy method, we prove that the traveling wavefronts are asymptotically stable in the weighted Banach spaces provided that the initial perturbations of the traveling wavefronts also belong to the same spaces.
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Keywords traveling wavefronts; monotone system; supersolution; subsolution; weighted energy estimate

Citation: Cheng-Hsiung Hsu, Jian-Jhong Lin, Shi-Liang Wu. Existence and stability of traveling wavefronts for discrete three species competitive-cooperative systems. Mathematical Biosciences and Engineering, 2019, 16(5): 4151-4181. doi: 10.3934/mbe.2019207


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