scholarly journals Population dynamical behavior of a single-species nonlinear diffusion system with random perturbation

2017 ◽  
Vol 67 (4) ◽  
pp. 867-890 ◽  
Author(s):  
Li Zu ◽  
Daqing Jiang ◽  
Donal O'Regan
Keyword(s):  
Nonlinear Diffusion ◽  
Random Perturbation ◽  
Dynamical Behavior ◽  
Single Species ◽  
Diffusion System

scholarly journals Stochastic Permanence, Stationary Distribution and Extinction of a Single-Species Nonlinear Diffusion System with Random Perturbation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Li Zu ◽  
Daqing Jiang ◽  
Donal O’Regan
Keyword(s):  
Numerical Simulation ◽  
Stationary Distribution ◽  
Nonlinear Diffusion ◽  
Logistic Model ◽  
Random Perturbation ◽  
Sufficient Conditions ◽  
Single Species ◽  
Unique Positive Solution ◽  
Stochastic Perturbations ◽  
Stochastic Permanence

We analyze the influence of stochastic perturbations on a single-species logistic model with the population’s nonlinear diffusion amongnpatches. First, we show that this system has a unique positive solution. Then we obtain sufficient conditions for stochastic permanence and persistence in mean, stationary distribution, and extinction. Finally, we illustrate our conclusions through numerical simulation.

Critical exponents for a nonlinear diffusion system

2007 ◽  
Vol 67 (4) ◽  
pp. 1190-1210 ◽  
Author(s):  
Sining Zheng ◽  
Wei Wang
Keyword(s):  
Critical Exponents ◽  
Nonlinear Diffusion ◽  
Diffusion System

POPULATION GROWTH MODELING WITH BOOM AND BUST PATTERNS: THE IMPULSIVE DIFFERENTIAL EQUATION FORMALISM

2015 ◽  
Vol 23 (supp01) ◽  
pp. S135-S149 ◽  
Author(s):  
FERNANDO CÓRDOVA-LEPE ◽  
GONZALO ROBLEDO ◽  
JAVIER CABRERA-VILLEGAS
Keyword(s):  
Differential Equation ◽  
Population Dynamics ◽  
Time Scales ◽  
Chaotic Dynamics ◽  
Impulsive Differential Equation ◽  
Dynamical Behavior ◽  
Single Species ◽  
Open Problems ◽  
Boom And Bust ◽  
Different Time Scales

This note gives an overview on basic mathematical models describing the population dynamics of a single species whose vital dynamics has different time scales. We present five cases combining two time–scales with Malthusian growth in at least one scale. The dynamical behavior shows a progressive complexity, from "naive" to chaotic dynamics (in the Li–Yorke's sense). In addition, some open problems and new results are presented.

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