Dynamical analysis and numerical simulations on a crowley-Martin predator-prey model in stochastic environment

2022 ◽  
Vol 413 ◽  
pp. 126641 ◽  
Author(s):  
Chun Lu
Keyword(s):  
Numerical Simulations ◽  
Dynamical Analysis ◽  
Stochastic Environment ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Feng Rao
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Functions ◽  
Allee Effect ◽  
Dynamical Analysis ◽  
Type Ii ◽  
Qualitative Properties ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Boundedness ◽  
Prey Model

We present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effect, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.

scholarly journals Dynamical Analysis of Predator-Prey Model Leslie-Gower with Omnivore

2018 ◽  
Vol 8 (2) ◽  
pp. 126-132
Author(s):  
Rina Exviani ◽  
◽  
Wuryansari Muharini Kusumawinahyu ◽  
Noor Hidayat
Keyword(s):  
Dynamical Analysis ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Dynamics of a Predator-Prey Model with Fear Effect and Time Delay

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Junli Liu ◽  
Pan Lv ◽  
Bairu Liu ◽  
Tailei Zhang
Keyword(s):  
Numerical Simulations ◽  
Dynamical Behavior ◽  
Normal Form Theory ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Predator Prey Model ◽  
Prey Model ◽  
Delay Dependent ◽  
The Impact ◽  
Dependent Factor

In this paper, we propose a time-delayed predator-prey model with Holling-type II functional response, which incorporates the gestation period and the cost of fear into prey reproduction. The dynamical behavior of this system is both analytically and numerically investigated from the viewpoint of stability, permanence, and bifurcation. We found that there are stability switches, and Hopf bifurcations occur when the delay τ passes through a sequence of critical values. The explicit formulae which determine the direction, stability, and other properties of the bifurcating periodic solutions are given by using the normal form theory and center manifold theorem. We perform extensive numerical simulations to explore the impact of some important parameters on the dynamics of the system. Numerical simulations show that high levels of fear have a stabilizing effect while relatively low levels of fear have a destabilizing effect on the predator-prey interactions which lead to limit-cycle oscillations. We also found that the model with or without a delay-dependent factor can have a significantly different dynamics. Thus, ignoring the delay or not including the delay-dependent factor might result in inaccurate modelling predictions.

Complex dynamic behaviors of a discrete predator–prey model with stage structure and harvesting

2016 ◽  
Vol 10 (01) ◽  
pp. 1750013 ◽  
Author(s):  
Boshan Chen ◽  
Jiejie Chen
Keyword(s):  
Numerical Simulations ◽  
Period Doubling ◽  
Stage Structure ◽  
Model Parameters ◽  
Flip Bifurcation ◽  
Predator Prey ◽  
Center Manifold Theorem ◽  
Predator Prey Model ◽  
Dynamical Behaviors ◽  
Prey Model

First, a discrete stage-structured and harvested predator–prey model is established, which is based on a predator–prey model with Type III functional response. Then theoretical methods are used to investigate existence of equilibria and their local properties. Third, it is shown that the system undergoes flip bifurcation and Neimark–Sacker bifurcation in the interior of [Formula: see text], by using the normal form of discrete systems, the center manifold theorem and the bifurcation theory, as varying the model parameters in some range. In particular, the direction and the stability of the flip bifurcation and the Neimark–Sacker bifurcation are showed. Finally, numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as cascades of period-doubling bifurcation and chaotic sets. These results reveal far richer dynamics of the discrete model compared with the continuous model. The Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. In addition, we show also the stabilizing effect of the harvesting by using numerical simulations.

Dynamical analysis of a stage-structured predator-prey model with cannibalism

2019 ◽  
Vol 307 ◽  
pp. 33-41 ◽  
Author(s):  
Fengqin Zhang ◽  
Yuming Chen ◽  
Jianquan Li
Keyword(s):  
Dynamical Analysis ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

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.

Sign in / Sign up

Export Citation Format

Share Document