GLOBAL DYNAMICS OF A POPULATION MODEL FROM RIVER ECOLOGY

Abstract We consider a parameter dependent parabolic logistic population model with diffusion and degenerate logistic term allowing for refuges for the population. The aim of the paper is to remove quite restrictive geometric and smoothness conditions on the refuge used in the existing literature. The key is a new simplified construction of a supersolution that does not make use of any regularity condition of the refuge. At the same time we also simplify other arguments commonly used in the literature.

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Global dynamics of a Lotka–Volterra competitive system from river ecology: general boundary conditions

Nonlinearity ◽

10.1088/1361-6544/ab60d8 ◽

2020 ◽

Vol 33 (4) ◽

pp. 1528-1541

Author(s):

Fangfang Xu ◽

Wenzhen Gan ◽

De Tang

Keyword(s):

Boundary Conditions ◽

General Boundary ◽

Global Dynamics ◽

General Boundary Conditions ◽

River Ecology ◽

Competitive System

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Bifurcations and global dynamics in a toxin-dependent aquatic population model

Mathematical Biosciences ◽

10.1016/j.mbs.2017.11.013 ◽

2018 ◽

Vol 296 ◽

pp. 26-35 ◽

Cited By ~ 1

Author(s):

Qihua Huang ◽

Gunog Seo ◽

Chunhua Shan

Keyword(s):

Population Model ◽

Global Dynamics

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The global dynamics of a discrete nonlinear hierarchical population system

International Journal of Biomathematics ◽

10.1142/s1793524519500220 ◽

2019 ◽

Vol 12 (02) ◽

pp. 1950022

Author(s):

Ze-Rong He ◽

Huai Chen ◽

Shu-Ping Wang

Keyword(s):

Dynamical Systems ◽

Lyapunov Function ◽

Population Model ◽

Numerical Experiments ◽

Discrete Dynamical Systems ◽

Reproductive Number ◽

Global Dynamics ◽

Population System ◽

The Stability ◽

Theoretical Results

This paper is concerned with the global dynamics of a hierarchical population model, in which the fertility of an individual depends on the total number of higher-ranking members. We investigate the stability of equilibria, nonexistence of periodic orbits and the persistence of the population by means of eigenvalues, Lyapunov function, and several results in discrete dynamical systems. Our work demonstrates that the reproductive number governs the evolution of the population. Besides the theoretical results, some numerical experiments are also presented.

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