BIFURCATION AND STABILITY OF A TWO-SPECIES DIFFUSIVE LOTKA-VOLTERRA MODEL

被引:13
作者
Ma, Li [1 ]
Guo, Shangjiang [2 ]
机构
[1] Gannan Normal Univ, Key Lab Jiangxi Prov Numer Simulat & Emulat Tech, Coll Math & Comp Sci, Ganzhou 341000, Jiangxi, Peoples R China
[2] China Univ Geosci, Sch Math & Phys, Wuhan 430074, Hubei, Peoples R China
基金
中国国家自然科学基金;
关键词
Coexistence; steady state; perturbation theory; comparison principle; bifurcation; Lyapunov-Schmidt reduction; PREDATOR-PREY MODEL; SPATIOTEMPORAL PATTERNS; STEADY-STATES; HOPF-BIFURCATION; COMPETITION MODEL; SYSTEM; DELAY; EQUATIONS; DYNAMICS; WAVE;
D O I
10.3934/cpaa.2020056
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:1205 / 1232
页数:28
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