scholarly journals The Dynamics of Sokol-Howell Prey-Predator Model Involving Strong Allee Effect

2021 ◽  
pp. 3114-3127
Author(s):  
Saad M. A. Al-Momen ◽  
Raid Kamil Naji
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Allee Effect ◽  
Pitchfork Bifurcation ◽  
Stability Conditions ◽  
Analytical Results ◽  
Saddle Node ◽  
Strong Allee Effect ◽  
Predator Model

In this paper,  a Sokol-Howell prey-predator model involving strong Allee effect is proposed and analyzed. The existence, uniqueness, and boundedness are studied. All the five possible equilibria have been are obtained and their local stability conditions are established. Using Sotomayor's theorem, the conditions of local saddle-node and transcritical and pitchfork bifurcation are derived and drawn. Numerical simulations are performed to clarify the analytical results

scholarly journals Enhancing synchrony in multiplex network due to rewiring frequency

2019 ◽  
Vol 475 (2230) ◽  
pp. 20190460 ◽  
Author(s):  
Sarbendu Rakshit ◽  
Bidesh K. Bera ◽  
Jürgen Kurths ◽  
Dibakar Ghosh
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Lorenz System ◽  
Stability Conditions ◽  
Network Architectures ◽  
Stability Function ◽  
Individual Layer ◽  
Multiplex Networks ◽  
Multiplex Network ◽  
Different Types

Most of the previous studies on synchrony in multiplex networks have been investigated using different types of intralayer network architectures which are either static or temporal. Effect of a temporal layer on intralayer synchrony in a multilayered network still remains elusive. In this paper, we discuss intralayer synchrony in a multiplex network consisting of static and temporal layers and how a temporal layer influences other static layers to enhance synchrony simultaneously. We analytically derive local stability conditions for intralayer synchrony based on the master stability function approach. The analytically derived results are illustrated by numerical simulations on up to five-layers multiplex networks with the paradigmatic Lorenz system as the node dynamics in each individual layer.

scholarly journals A Prey-Predator Model with Michael Mentence Type of Predator Harvesting and Infectious Disease in Prey

2020 ◽  
pp. 1146-1163
Author(s):  
Hiba Abdullah Ibrahim ◽  
Raid Kamel Naji
Keyword(s):  
Infectious Disease ◽  
Numerical Simulations ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Local Bifurcation ◽  
Persistence Conditions ◽  
Analytical Results ◽  
Predator Model ◽  
Disease In Prey

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

scholarly journals Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Chunshan Xue ◽  
Xia Liu
Keyword(s):  
Food Chain ◽  
Allee Effect ◽  
Complex Dynamics ◽  
Period Doubling ◽  
Biological Phenomenon ◽  
Chain System ◽  
Saddle Node ◽  
Strong Allee Effect

Allee effect, as an important biological phenomenon, has been considered in many ecosystems, whereas, its influence on interactions of three or more species is little investigated. In this paper we modify a three-species Leslie-Gower type food chain system by incorporating the strong Allee effect into the source. Our results show that the existence of Allee effect contributes to the occurrence of more complex dynamics of the system, including Hopf, saddle-node, transcritical, saddle-node-Hopf, period-doubling, and period-halving bifurcations and chaos.

scholarly journals Stability Analysis of a Fractional Order Modified Leslie-Gower Model with Additive Allee Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Agus Suryanto ◽  
Isnani Darti ◽  
Syaiful Anam
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Local Stability ◽  
Allee Effect ◽  
Dynamical Behavior ◽  
Continuous Model ◽  
Positivity Of Solutions ◽  
Existence Conditions ◽  
Dynamical Properties

We analyze the dynamics of a fractional order modified Leslie-Gower model with Beddington-DeAngelis functional response and additive Allee effect by means of local stability. In this respect, all possible equilibria and their existence conditions are determined and their stability properties are established. We also construct nonstandard numerical schemes based on Grünwald-Letnikov approximation. The constructed scheme is explicit and maintains the positivity of solutions. Using this scheme, we perform some numerical simulations to illustrate the dynamical behavior of the model. It is noticed that the nonstandard Grünwald-Letnikov scheme preserves the dynamical properties of the continuous model, while the classical scheme may fail to maintain those dynamical properties.

Rich Global Dynamics in a Prey–Predator Model with Allee Effect and Density Dependent Death Rate of Predator

2015 ◽  
Vol 25 (03) ◽  
pp. 1530007 ◽  
Author(s):  
Moitri Sen ◽  
Malay Banerjee
Keyword(s):  
Death Rate ◽  
Allee Effect ◽  
Growth Function ◽  
Global Dynamics ◽  
Density Dependent ◽  
Strong Allee Effect ◽  
Local And Global Bifurcations ◽  
Predator Model ◽  
Type Ii Functional Response ◽  
Comprehensive Study

In this work we have considered a prey–predator model with strong Allee effect in the prey growth function, Holling type-II functional response and density dependent death rate for predators. It presents a comprehensive study of the complete global dynamics for the considered system. Especially to see the effect of the density dependent death rate of predator on the system behavior, we have presented the two parametric bifurcation diagrams taking it as one of the bifurcation parameters. In course of that we have explored all possible local and global bifurcations that the system could undergo, namely the existence of transcritical bifurcation, saddle node bifurcation, cusp bifurcation, Hopf-bifurcation, Bogdanov–Takens bifurcation and Bautin bifurcation respectively.

A competition model with herd behaviour and allee effect

Filomat ◽  
2019 ◽  
Vol 33 (8) ◽  
pp. 2529-2542
Author(s):  
Prosenjit Sen ◽  
Alakes Maiti ◽  
G.P. Samanta
Keyword(s):  
Time Delay ◽  
Numerical Simulations ◽  
Discrete Time ◽  
Local Stability ◽  
Allee Effect ◽  
Equilibrium Points ◽  
Uniform Boundedness ◽  
Competition Model ◽  
Discrete Time Delay ◽  
Herd Behaviour

In this work we have studied the deterministic behaviours of a competition model with herd behaviour and Allee effect. The uniform boundedness of the system has been studied. Criteria for local stability at equilibrium points are derived. The effect of discrete time-delay on the model is investigated. We have carried out numerical simulations to validate the analytical findings. The biological implications of our analytical and numerical findings are discussed.

Bifurcation analysis in a predator–prey model with strong Allee effect

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jingwen Zhu ◽  
Ranchao Wu ◽  
Mengxin Chen
Keyword(s):  
Allee Effect ◽  
Phase Portraits ◽  
Allee Effects ◽  
Saddle Node Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Saddle Node ◽  
Existence And Stability ◽  
Strong Allee Effect

Abstract In this paper, strong Allee effects on the bifurcation of the predator–prey model with ratio-dependent Holling type III response are considered, where the prey in the model is subject to a strong Allee effect. The existence and stability of equilibria and the detailed behavior of possible bifurcations are discussed. Specifically, the existence of saddle-node bifurcation is analyzed by using Sotomayor’s theorem, the direction of Hopf bifurcation is determined, with two bifurcation parameters, the occurrence of Bogdanov–Takens of codimension 2 is showed through calculation of the universal unfolding near the cusp. Comparing with the cases with a weak Allee effect and no Allee effect, the results show that the Allee effect plays a significant role in determining the stability and bifurcation phenomena of the model. It favors the coexistence of the predator and prey, can lead to more complex dynamical behaviors, not only the saddle-node bifurcation but also Bogdanov–Takens bifurcation. Numerical simulations and phase portraits are also given to verify our theoretical analysis.

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