scholarly journals A Predator-Prey Model In Deterministic And Stochastic Environments

2021 ◽  
Author(s):  
Chandra P. Limbu
Keyword(s):  
Numerical Simulations ◽  
Ecological Systems ◽  
Volterra Model ◽  
Phase Portraits ◽  
Hopf Bifurcations ◽  
Stochastic Environment ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Environments ◽  
Uniqueness Of Limit Cycles

We investigate the phase portraits, the uniqueness of limit cycles and the Hopf bifurcations in the Holling-Tanner models in deterministic and stochastic environments. We provide the conditions on the parameters to assure saddle, focus and node. We use numerical simulations to demonstrate our results in the deterministic cases. We also explore the Holling-Tanner model in a stochastic environment by using numerical simulations. We generalize and improve some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems.

scholarly journals A Predator-Prey Model In Deterministic And Stochastic Environments

2021 ◽  
Author(s):  
Chandra P. Limbu
Keyword(s):  
Numerical Simulations ◽  
Ecological Systems ◽  
Volterra Model ◽  
Phase Portraits ◽  
Hopf Bifurcations ◽  
Stochastic Environment ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Environments ◽  
Uniqueness Of Limit Cycles

We investigate the phase portraits, the uniqueness of limit cycles and the Hopf bifurcations in the Holling-Tanner models in deterministic and stochastic environments. We provide the conditions on the parameters to assure saddle, focus and node. We use numerical simulations to demonstrate our results in the deterministic cases. We also explore the Holling-Tanner model in a stochastic environment by using numerical simulations. We generalize and improve some new results on Holling-Tanner model from Lotka-Volterra model on real ecological systems.

scholarly journals Bifurcation and Chaos of a Discrete Predator-Prey Model with Crowley–Martin Functional Response Incorporating Proportional Prey Refuge

2020 ◽  
Vol 2020 ◽  
pp. 1-18 ◽  
Author(s):  
P. K. Santra ◽  
G. S. Mahapatra ◽  
G. R. Phaijoo
Keyword(s):  
Functional Response ◽  
Control Method ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Phase Portraits ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Feedback Control Method ◽  
And Control

The paper investigates the dynamical behaviors of a two-species discrete predator-prey system with Crowley–Martin functional response incorporating prey refuge proportional to prey density. The existence of equilibrium points, stability of three fixed points, period-doubling bifurcation, Neimark–Sacker bifurcation, Marottos chaos, and Control Chaos are analyzed for the discrete-time domain. The time graphs, phase portraits, and bifurcation diagrams are obtained for different parameters of the model. Numerical simulations and graphics show that the discrete model exhibits rich dynamics, which also present that the system is a chaotic and complex one. This paper attempts to present a feedback control method which can stabilize chaotic orbits at an unstable equilibrium point.

On the Bifurcation Structure of a Leslie–Tanner Model with a Generalist Predator

2020 ◽  
Vol 30 (06) ◽  
pp. 2050088
Author(s):  
Luis Miguel Valenzuela ◽  
Gamaliel Blé ◽  
Manuel Falconi
Keyword(s):  
Generalist Predator ◽  
Hopf Bifurcations ◽  
Stable Limit ◽  
Previous Knowledge ◽  
Bifurcation Structure ◽  
Remarkable Feature ◽  
Predator Prey ◽  
Predator Prey Model ◽  
The Subject ◽  
Stable Limit Cycles

In this work, the dynamical properties of a Leslie–Tanner predator–prey model are analyzed. A method is provided to find the regions in the parameter space where Bautin, Hopf and simultaneous supercritical Hopf bifurcations exist. A remarkable feature of the dynamics of the model is the existence of tristability. In fact, the system simultaneously presents three stable limit cycles. These results generalize some previous knowledge on the subject since both prey defense and a generalist predator are incorporated in our analysis.

Solitary waves in excitable systems with cross-diffusion

2005 ◽  
Vol 461 (2064) ◽  
pp. 3711-3730 ◽  
Author(s):  
Vadim N Biktashev ◽  
Mikhail A Tsyganov
Keyword(s):  
Asymptotic Behaviour ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
System Of Equations ◽  
Soliton Interaction ◽  
Predator Prey ◽  
Self Diffusion ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Excitable Systems

We consider a FitzHugh–Nagumo system of equations where the traditional diffusion terms are replaced with linear cross-diffusion of components. This system describes solitary waves that have unusual form and are capable of quasi-soliton interaction. This is different from the classical FitzHugh–Nagumo system with self-diffusion, but similar to a predator–prey model with taxis of populations on each other's gradient which we considered earlier. We study these waves by numerical simulations and also present an analytical theory, based on the asymptotic behaviour which arises when the local dynamics of the inhibitor field are much slower than those of the activator field.

scholarly journals Effects of Behavioral Tactics of Predators on Dynamics of a Predator-Prey System

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Hui Zhang ◽  
Zhihui Ma ◽  
Gongnan Xie ◽  
Lukun Jia
Keyword(s):  
Time Scale ◽  
Stable State ◽  
Volterra Model ◽  
Fast Time ◽  
Predator Population ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Prey Interaction ◽  
Game Dynamic

A predator-prey model incorporating individual behavior is presented, where the predator-prey interaction is described by a classical Lotka-Volterra model with self-limiting prey; predators can use the behavioral tactics of rock-paper-scissors to dispute a prey when they meet. The predator behavioral change is described by replicator equations, a game dynamic model at the fast time scale, whereas predator-prey interactions are assumed acting at a relatively slow time scale. Aggregation approach is applied to combine the two time scales into a single one. The analytical results show that predators have an equal probability to adopt three strategies at the stable state of the predator-prey interaction system. The diversification tactics taking by predator population benefits the survival of the predator population itself, more importantly, it also maintains the stability of the predator-prey system. Explicitly, immediate contest behavior of predators can promote density of the predator population and keep the preys at a lower density. However, a large cost of fighting will cause not only the density of predators to be lower but also preys to be higher, which may even lead to extinction of the predator populations.

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