Journal
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
Volume 19, Issue 3, Pages 1205-1232Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/cpaa.2020056
Keywords
Coexistence; steady state; perturbation theory; comparison principle; bifurcation; Lyapunov-Schmidt reduction
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Funding
- Jiangxi Science and Technology Project [GJJ170844]
- National Natural Science Foundation of China [11671123, 11801089, 11901110]
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This paper is devoted to a two-species Lotka-Volterra model with general functional response. The existence, local and global stability of boundary (including trivial and semi-trivial) steady-state solutions are analyzed by means of the signs of the associated principal eigenvalues. Moreover, the nonexistence and steady-state bifurcation of coexistence steady-state solutions at each of the boundary steady states are investigated. In particular, the coincidence of bifurcating coexistence steady-state solution branches is also described. It should be pointed out that the methods we applied here are mainly based on spectral analysis, perturbation theory, comparison principle, monotone theory, Lyapunov-Schmidt reduction, and bifurcation theory.
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