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.

Dynamic analysis of a fractional order system

2015 ◽  
Vol 08 (06) ◽  
pp. 1550079
Author(s):  
M. Javidi ◽  
N. Nyamoradi
Keyword(s):  
Stability Analysis ◽  
Fractional Derivative ◽  
Dynamic Analysis ◽  
Fractional Order ◽  
Local Stability ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Order System ◽  
Stability Conditions ◽  
Hurwitz Stability

In this paper, we investigate the dynamical behavior of a fractional order phytoplankton–zooplankton system. In this paper, stability analysis of the phytoplankton–zooplankton model (PZM) is studied by using the fractional Routh–Hurwitz stability conditions. We have studied the local stability of the equilibrium points of PZM. We applied an efficient numerical method based on converting the fractional derivative to integer derivative to solve the PZM.

A fractional-order toxin producing phytoplankton and zooplankton system

2014 ◽  
Vol 07 (04) ◽  
pp. 1450039 ◽  
Author(s):  
M. Javidi ◽  
N. Nyamoradi
Keyword(s):  
Stability Analysis ◽  
Nutrient Cycling ◽  
Fractional Order ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Stability Conditions ◽  
Hurwitz Stability ◽  
Local Stability Analysis ◽  
Mathematical System ◽  
Parameter Values

In this work, we investigate the dynamical behavior of a fractional-order toxin producing on a phytoplankton–zooplankton (TPPZ) system with nutrient cycling. We propose a mathematical system to model this situation. All the feasible equilibria of the system are obtained and the conditions for the existence of the equilibriums are determined. Local stability analysis of the TPPZ is studied by using the fractional Routh–Hurwitz stability conditions. Numerical simulations are carried out for a hypothetical set of parameter values to substantiate our analytical findings.

Optimal Synchronization of a Memristive Chaotic Circuit

2016 ◽  
Vol 26 (06) ◽  
pp. 1650093 ◽  
Author(s):  
Michaux Kountchou ◽  
Patrick Louodop ◽  
Samuel Bowong ◽  
Hilaire Fotsin ◽  
Jurgen Kurths
Keyword(s):  
Numerical Simulations ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Analog Circuit ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Dynamical Properties ◽  
Analog Circuit Implementation

This paper deals with the problem of optimal synchronization of two identical memristive chaotic systems. We first study some basic dynamical properties and behaviors of a memristor oscillator with a simple topology. An electronic circuit (analog simulator) is proposed to investigate the dynamical behavior of the system. An optimal synchronization strategy based on the controllability functions method with a mixed cost functional is investigated. A finite horizon is explicitly computed such that the chaos synchronization is achieved at an established time. Numerical simulations are presented to verify the effectiveness of the proposed synchronization strategy. Pspice analog circuit implementation of the complete master-slave-controller systems is also presented to show the feasibility of the proposed scheme.

More Dynamical Properties Revealed from a 3D Lorenz-like System

2014 ◽  
Vol 24 (10) ◽  
pp. 1450133 ◽  
Author(s):  
Haijun Wang ◽  
Xianyi Li
Keyword(s):  
Numerical Simulations ◽  
Local Stability ◽  
Equilibrium Points ◽  
Heteroclinic Orbits ◽  
Mathematical Work ◽  
Chaotic Attractors ◽  
Heteroclinic Cycles ◽  
Homoclinic And Heteroclinic Orbits ◽  
Dynamical Properties ◽  
Theoretical Results

After a 3D Lorenz-like system has been revisited, more rich hidden dynamics that was not found previously is clearly revealed. Some more precise mathematical work, such as for the complete distribution and the local stability and bifurcation of its equilibrium points, the existence of singularly degenerate heteroclinic cycles as well as homoclinic and heteroclinic orbits, and the dynamics at infinity, is carried out in this paper. In particular, another possible new mechanism behind the creation of chaotic attractors is presented. Based on this mechanism, some different structure types of chaotic attractors are numerically found in the case of small b > 0. All theoretical results obtained are further illustrated by numerical simulations. What we formulate in this paper is to not only show those dynamical properties hiding in this system, but also (more mainly) present a kind of way and means — both "locally" and "globally" and both "finitely" and "infinitely" — to comprehensively explore a given system.

scholarly journals A Mathematical Model to Study the Effectiveness of Some of the Strategies Adopted in Curtailing the Spread of COVID-19

2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Isa Abdullahi Baba ◽  
Bashir Abdullahi Baba ◽  
Parvaneh Esmaili
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Numerical Simulations ◽  
Government Policy ◽  
Local Stability ◽  
Equilibrium Points ◽  
Compartmental Models ◽  
Effective Strategy ◽  
Local Stability Analysis ◽  
The Government

In this paper, we developed a model that suggests the use of robots in identifying COVID-19-positive patients and which studied the effectiveness of the government policy of prohibiting migration of individuals into their countries especially from those countries that were known to have COVID-19 epidemic. Two compartmental models consisting of two equations each were constructed. The models studied the use of robots for the identification of COVID-19-positive patients. The effect of migration ban strategy was also studied. Four biologically meaningful equilibrium points were found. Their local stability analysis was also carried out. Numerical simulations were carried out, and the most effective strategy to curtail the spread of the disease was shown.

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

DYNAMICS OF A SEGMENTATION CLOCK MODEL WITH DISCRETE AND DISTRIBUTED DELAYS

2010 ◽  
Vol 03 (04) ◽  
pp. 399-416 ◽  
Author(s):  
PENG FENG
Keyword(s):  
Stability Analysis ◽  
Numerical Simulations ◽  
Local Stability ◽  
Time Delays ◽  
Distributed Delay ◽  
Distributed Delays ◽  
Clock Model ◽  
Segmentation Clock ◽  
Local Stability Analysis ◽  
First Case

In this paper, we study the effects of time delays on the dynamics of a segmentation clock model with both discrete and distributed delays. Two cases are considered. The first case corresponds to the model with only distributed delay. The second case involves both discrete and distributed delay. Local stability analysis is carried out for all cases. Numerical simulations are also performed to illustrate the results.

scholarly journals Stability Analysis for a Fractional HIV Infection Model with Nonlinear Incidence

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Linli Zhang ◽  
Gang Huang ◽  
Anping Liu ◽  
Ruili Fan
Keyword(s):  
Population Dynamics ◽  
Stability Analysis ◽  
Hiv Infection ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Nonnegative Solution ◽  
Infection Model ◽  
Nonlinear Incidence ◽  
Hiv Infection Model ◽  
The Stability

We introduce the fractional-order derivatives into an HIV infection model with nonlinear incidence and show that the established model in this paper possesses nonnegative solution, as desired in any population dynamics. We also deal with the stability of the infection-free equilibrium, the immune-absence equilibrium, and the immune-presence equilibrium. Numerical simulations are carried out to illustrate the results.

scholarly journals Dynamical Behavior and Stability Analysis in a Hybrid Epidemiological-Economic Model with Incubation

2014 ◽  
Vol 2014 ◽  
pp. 1-22 ◽  
Author(s):  
Chao Liu ◽  
Wenquan Yue ◽  
Peiyong Liu
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Dynamical Behavior ◽  
Model System ◽  
Host Population ◽  
Economic Interest ◽  
Susceptible Host ◽  
Interior Equilibrium

A hybrid SIR vector disease model with incubation is established, where susceptible host population satisfies the logistic equation and the recovered host individuals are commercially harvested. It is utilized to discuss the transmission mechanism of infectious disease and dynamical effect of commercial harvest on population dynamics. Positivity and permanence of solutions are analytically investigated. By choosing economic interest of commercial harvesting as a parameter, dynamical behavior and local stability of model system without time delay are studied. It reveals that there is a phenomenon of singularity induced bifurcation as well as local stability switch around interior equilibrium when economic interest increases through zero. State feedback controllers are designed to stabilize model system around the desired interior equilibria in the case of zero economic interest and positive economic interest, respectively. By analyzing corresponding characteristic equation of model system with time delay, local stability analysis around interior equilibrium is discussed due to variation of time delay. Hopf bifurcation occurs at the critical value of time delay and corresponding limit cycle is also observed. Furthermore, directions of Hopf bifurcation and stability of the bifurcating periodic solutions are studied. Numerical simulations are carried out to show consistency with theoretical analysis.

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