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- Title
Qualitative Analysis of a Single-Species Model with Distributed Delay and Nonlinear Harvest.
- Authors
Li, Zuxiong; Fu, Shengnan; Xiang, Huili; Wang, Hailing
- Abstract
In this paper, a single-species population model with distributed delay and Michaelis-Menten type harvesting is established. Through an appropriate transformation, the mathematical model is converted into a two-dimensional system. Applying qualitative theory of ordinary differential equations, we obtain sufficient conditions for the stability of the equilibria of this system under three cases. The equilibrium A 1 of system is globally asymptotically stable when b r − c > 0 and η < 0 . Using Poincare-Bendixson theorem, we determine the existence and stability of limit cycle when b r − c > 0 and η > 0 . By computing Lyapunov number, we obtain that a supercritical Hopf bifurcation occurs when η passes through 0. High order singularity of the system, such as saddle node, degenerate critical point, unstable node, saddle point, etc, is studied by the theory of ordinary differential equations. Numerical simulations are provided to verify our main results in this paper.
- Subjects
ORDINARY differential equations; LIMIT cycles; HOPF bifurcations; MATHEMATICAL models; CRITICAL point (Thermodynamics); COMPUTER simulation
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 20, p2560
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9202560