Dynamic of a delayed predator–prey model with birth pulse and impulsive harvesting in a polluted environment

2015 ◽  
Vol 422 ◽  
pp. 1-15 ◽  
Author(s):  
Xiaohong Wang ◽  
Jianwen Jia
Keyword(s):  
Polluted Environment ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Birth Pulse ◽  
Prey Model ◽  
Impulsive Harvesting

Persistence and extinction of a stochastic delay predator-prey model in a polluted environment

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
Zhenhai Liu ◽  
Qun Liu
Keyword(s):  
Numerical Simulations ◽  
Critical Value ◽  
Polluted Environment ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Persistence In The Mean ◽  
The Mean

AbstractIn this paper, we study a stochastic delay predator-prey model in a polluted environment. Sufficient criteria for extinction and non-persistence in the mean of the model are obtained. The critical value between persistence and extinction is also derived for each population. Finally, some numerical simulations are provided to support our main results.

DYNAMICAL ANALYSIS OF A THREE-DIMENSIONAL PREDATOR-PREY MODEL WITH IMPULSIVE HARVESTING AND DIFFUSION

2011 ◽  
Vol 21 (02) ◽  
pp. 453-465 ◽  
Author(s):  
JIANJUN JIAO ◽  
SHAOHONG CAI ◽  
LANSUN CHEN
Keyword(s):  
Three Dimensional ◽  
Dynamical Analysis ◽  
Biological Resource ◽  
Globally Asymptotically Stable ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
All Solutions ◽  
And Diffusion ◽  
Impulsive Harvesting

In this work, we consider a three-dimensional predator-prey model with impulsive harvesting and diffusion at different fixed moments. We prove that all solutions of the investigated system are uniformly ultimately bounded. The conditions of the globally asymptotically stable prey-extinction boundary periodic solution of the investigated system are obtained, as well the permanence of the investigated system. Finally, numerical analysis is inserted to illustrate the results which provide reliable tactic basis for the practical biological resource management.

scholarly journals Analysis of Stochastic Delay Predator-Prey System with Impulsive Toxicant Input in Polluted Environments

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Meng Liu
Keyword(s):  
Polluted Environment ◽  
Stochastic Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Model ◽  
Time Average

A stochastic delay predator-prey model in a polluted environment with impulsive toxicant input is proposed and studied. The thresholds between stability in time average and extinction of each population are obtained. Some recent results are extended and improved greatly. Several simulation figures are introduced to support the conclusions.

scholarly journals Survival and ergodicity of a stochastic Holling-III predator–prey model with Markovian switching in an impulsive polluted environment

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Wen Qin ◽  
Hanjun Zhang ◽  
Qingsong He
Keyword(s):  
Existence And Uniqueness ◽  
Lyapunov Functions ◽  
Colored Noise ◽  
Polluted Environment ◽  
Existence And Uniqueness Theorem ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Theoretical Results

AbstractBased on the effects of white noise and colored noise, we propose a stochastic Holling-III predator–prey model in an impulsive polluted environment. Firstly, we prove an existence and uniqueness theorem of the presented model. Secondly, we establish sufficient criteria of extinction, nonpersistence in mean, and weak persistence in mean for both prey and predator species. Thirdly, with the aid of Lyapunov functions, we prove that this system is ergodic and has a unique stationary distribution under certain conditions. Finally, we verify the theoretical results by performing some numerical simulations.

DYNAMIC COMPLEXITIES IN RATIO-DEPENDENT PREDATOR–PREY ECOSYSTEM MODELS WITH BIRTH PULSE AND PESTICIDE PULSE

2004 ◽  
Vol 14 (08) ◽  
pp. 2893-2903 ◽  
Author(s):  
JING HUI ◽  
LAN-SUN CHEN
Keyword(s):  
Discrete Dynamical System ◽  
Period Doubling ◽  
Ecosystem Models ◽  
Pest Population ◽  
Natural Period ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Birth Pulse ◽  
Prey Model ◽  
Ratio Dependent

In many models of pest control, increases in pest population due to birth are assumed to be continuous, but in fact, pest population reproduces only during a single period; at the same time, pesticides are often applied during the period. So in this paper we propose a ratio-dependent predator–prey model with birth pulse and pesticide pulse. Using the discrete dynamical system determined by the stroboscopic map, we obtain an exact periodic solution of systems which have Ricker functions or Beverton–Holt functions, and obtain the threshold conditions for their stability. Above the threshold, there is a characteristic sequence of bifurcations, leading to chaotic dynamics, which implies that the dynamical behaviors of the ratio-dependent predator–prey model with birth pulse and pesticide pulse are very complex, including small-amplitude oscillations, large-amplitude cycles and chaos. This suggests that birth pulse and pesticide pulse, in effect, provide a natural period or cyclicity that allows for period-doubling bifurcation and period-halving bifurcation route to chaos.

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