scholarly journals Existence and stability of traveling waves for Leslie-Gower predator-prey system with nonlocal diffusion

2017 ◽  
Vol 37 (10) ◽  
pp. 5433-5454 ◽  
Author(s):  
Hongmei Cheng ◽  
◽  
Rong Yuan ◽  
Keyword(s):  
Traveling Waves ◽  
Nonlocal Diffusion ◽  
Predator Prey ◽  
Prey System ◽  
Existence And Stability

scholarly journals Investigation on dynamics of an impulsive predator–prey system with generalized Holling type IV functional response and anti-predator behavior

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Nattawut Khansai ◽  
Akapak Charoenloedmongkhon
Keyword(s):  
Periodic Solution ◽  
Functional Response ◽  
Impulsive Control ◽  
Positive Periodic Solution ◽  
Existence Condition ◽  
Predator Prey ◽  
Type Iv ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Behavior

AbstractIn the present article, we propose and analyze a new mathematical model for a predator–prey system including the following terms: a Monod–Haldane functional response (a generalized Holling type IV), a term describing the anti-predator behavior of prey populations and one for an impulsive control strategy. In particular, we establish the existence condition under which the system has a locally asymptotically stable prey-eradication periodic solution. Violating such a condition, the system turns out to be permanent. Employing bifurcation theory, some conditions, under which the existence and stability of a positive periodic solution of the system occur but its prey-eradication periodic solution becomes unstable, are provided. Furthermore, numerical simulations for the proposed model are given to confirm the obtained theoretical results.

scholarly journals Modeling the Phenomenon of Xenophobia in Africa

2021 ◽  
Vol 53 (2) ◽  
pp. 261-285
Author(s):  
Reuben Iortyer Gweryina ◽  
Emilian Chinwendu Madubueze ◽  
Simon James Ogaji
Keyword(s):  
Period Doubling ◽  
Critical Parameters ◽  
Predator Prey ◽  
Prey System ◽  
Existence And Stability ◽  
Group Defense ◽  
Effective Group ◽  
Coexistence State ◽  
Globally Stable ◽  
Special Case

In this study, we applied the principle of a competitive predator-prey system to propose a prey-predator-like model of xenophobia in Africa. The boundedness of the solution, the existence and stability of equilibrium states of the xenophobic model are discussed accordingly. As a special case, the coexistence state was found to be locally and globally stable based on the parametric conditions of effective group defense and anti-xenophobic policy implementation. The system was further analyzed by Sotomayor’s theory to show that each equilibrium point bifurcates transcritically. However, numerical proof showed period-doubling bifurcation, which makes the xenophobic situation more chaotic in Africa. Further numerical simulations support the analytical results with the view that tolerance, group defense and anti-xenophobic policies are critical parameters for the coexistence of foreigners and xenophobes.

scholarly journals Comparison and analysis of two forms of harvesting functions in the two-prey and one-predator model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xinxin Liu ◽  
Qingdao Huang
Keyword(s):  
Prey Species ◽  
Equilibrium Points ◽  
Maximum Sustainable Yield ◽  
Predator Prey ◽  
Prey System ◽  
Existence And Stability ◽  
Predator Model ◽  
Model Equations ◽  
The Given

AbstractA new way to study the harvested predator–prey system is presented by analyzing the dynamics of two-prey and one-predator model, in which two teams of prey are interacting with one team of predators and the harvesting functions for two prey species takes different forms. Firstly, we make a brief analysis of the dynamics of the two subsystems which include one predator and one prey, respectively. The positivity and boundedness of the solutions are verified. The existence and stability of seven equilibrium points of the three-species model are further studied. Specifically, the global stability analysis of the coexistence equilibrium point is investigated. The problem of maximum sustainable yield and dynamic optimal yield in finite time is studied. Numerical simulations are performed using MATLAB from four aspects: the role of the carrying capacity of prey, the simulation about the model equations around three biologically significant steady states, simulation for the yield problem of model system, and the comparison between the two forms of harvesting functions. We obtain that the new form of harvesting function is more realistic than the traditional form in the given model, which may be a better reflection of the role of human-made disturbance in the development of the biological system.

scholarly journals Dynamic Analysis of Beddington–DeAngelis Predator-Prey System with Nonlinear Impulse Feedback Control

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Dezhao Li ◽  
Huidong Cheng ◽  
Yu Liu
Keyword(s):  
Periodic Solution ◽  
Feedback Control ◽  
Control Period ◽  
Sufficient Conditions ◽  
Parameter Analysis ◽  
Pest Population ◽  
Predator Prey ◽  
Prey System ◽  
Threshold Conditions ◽  
Existence And Stability

In this paper, a predator-prey system with pesticide dose-responded nonlinear pulse of Beddington–DeAngelis functional response is established. First, we construct the Poincaré map of the impulsive semidynamic system and discuss its main properties including the monotonicity, differentiability, fixed point, and asymptote. Second, we address the existence and globally asymptotic stability of the order-1 periodic solution and the sufficient conditions for the existence of the order-k(k ≥ 2) periodic solution. Thirdly, we give the threshold conditions for the existence and stability of boundary periodic solutions and present the parameter analysis. The results show that the pesticide dosage increases with the extension of the control period and decreases with the increase of the threshold. Besides, the state pulse feedback control can manage the pest population at a certain level and avoid excessive application of pesticides.

Topological Horseshoes of Traveling Waves for a Fast–Slow Predator–Prey System

2006 ◽  
Vol 19 (3) ◽  
pp. 623-654 ◽  
Author(s):  
Marcio Gameiro ◽  
Tomáš Gedeon ◽  
William Kalies ◽  
Hiroshi Kokubu ◽  
Konstantin Mischaikow ◽  
...  
Keyword(s):  
Traveling Waves ◽  
Predator Prey ◽  
Prey System ◽  
Topological Horseshoes

scholarly journals Transitional Periodic Patterns and Triple Attractors in a Predator-Prey System with Fear and Refuge

2022 ◽  
Author(s):  
Shilpa Garai ◽  
N. C. Pati ◽  
G. C. Layek ◽  
Nikhil Pal
Keyword(s):  
Periodic Structures ◽  
Largest Lyapunov Exponent ◽  
Present System ◽  
Periodic Patterns ◽  
Parameter Spaces ◽  
Predator Prey ◽  
System A ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Existence And Stability

Abstract We report the existence of periodic structures in the transitional and chaotic regimes in bi-parameter spaces of a predator-prey system. A model is constructed taking into consideration of two important effects: namely, the prey refuge and fear of predation risk. The fixed points, their existence and stability behaviors are analyzed. The Neimark-Sacker bifurcation in the neighborhood of the interior fixed point is shown selecting refuge strength as a bifurcation parameter. The complex dynamical behaviors are explored in the biparameter space with the help of the largest Lyapunov exponent and isoperiodic diagrams. The period-bubbling transitional patterns, and triple heterogeneous attractors resulting in qualitative unpredictability are identified in the present system. The Wada basin sets for the triple coexisting attractors are found. The study reveals that the oscillations of the populations in certain control parameter regions are highly dependent upon the initial densities of the populations.

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