scholarly journals The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

2022 ◽  
Vol 7 (4) ◽  
pp. 5463-5479
Author(s):  
Ali Yousef ◽  
◽  
Ashraf Adnan Thirthar ◽  
Abdesslem Larmani Alaoui ◽  
Prabir Panja ◽  
...  
Keyword(s):  
Fractional Order ◽  
Equation System ◽  
Order System ◽  
Differential Equation System ◽  
Order Model ◽  
Predator Prey ◽  
Fear Effect ◽  
Fractional Order Model ◽  
Prey Interaction ◽  
The Stability

<abstract><p>This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.</p></abstract>

scholarly journals Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Ruiqing Shi ◽  
Ting Lu ◽  
Cuihong Wang
Keyword(s):  
Hepatitis B Virus ◽  
Hepatitis B ◽  
Fractional Order ◽  
Reproduction Number ◽  
Sufficient Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
B Virus ◽  
The Stability ◽  
Holling Ii Functional Response

In this paper, a fractional-order model is constructed to describe the transmission of Hepatitis B Virus (HBV). Firstly, the existence and uniqueness of positive solutions are proved. Secondly, the basic reproduction number and the sufficient conditions for the existence of two equilibriums are obtained. Thirdly, the stability of equilibriums are analyzed. After that, some numerical simulations are performed to verify the theoretical prediction. Finally, a brief discussion is presented.

Multistability and Coexisting Attractors in a New Circulant Chaotic System

2019 ◽  
Vol 29 (13) ◽  
pp. 1950174 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
Fawaz E. Alsaadi ◽  
Fahimeh Nazarimehr ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Chaotic Flow ◽  
Fractional Order Model ◽  
Dynamical Properties ◽  
Fractional Orders

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various fractional orders. Bifurcation analysis of the fractional order system shows that it has a kind of multistability like the integer order system, which is a very rare phenomenon. Circuit realization of the proposed system is also carried out to show that it is usable for engineering applications.

scholarly journals A Fractional-Order Model of COVID-19 considering the Fear Effect of the Media and Social Networks on the Community

2021 ◽  
pp. 111403
Author(s):  
Fatma Bozkurt ◽  
Ali Yousef ◽  
Thabet Abdeljawad ◽  
Adem Kalinli ◽  
Qasem Al Mdallal
Keyword(s):  
Social Networks ◽  
Fractional Order ◽  
Order Model ◽  
Fear Effect ◽  
Fractional Order Model ◽  
The Media

scholarly journals Fractional-Order Model of Two-Prey One-Predator System

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mohammed Fathy Elettreby ◽  
Ahlam Abdullah Al-Raezah ◽  
Tamer Nabil
Keyword(s):  
Asymptotic Stability ◽  
Fractional Order ◽  
Equilibrium Solution ◽  
Order System ◽  
Asymptotically Stable ◽  
Equilibrium Solutions ◽  
Order Model ◽  
Local Asymptotic Stability ◽  
Fractional Order Model ◽  
Predator System

We propose a fractional-order model of the interaction within two-prey and one-predator system. We prove the existence and the uniqueness of the solutions of this model. We investigate in detail the local asymptotic stability of the equilibrium solutions of this model. Also, we illustrate the analytical results by some numerical simulations. Finally, we give an example of an equilibrium solution that is centre for the integer order system, while it is locally asymptotically stable for its fractional-order counterpart.

scholarly journals A fractional-order love dynamical model with time delay for synergic couple : Stability analysis and Hopf bifurcation

2021 ◽  
Author(s):  
SANTOSHI PANIGRAHI ◽  
Sunita Chand ◽  
S Balamuralitharan
Keyword(s):  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Fractional Order ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
The Impact

We investigate the fractional order love dynamic model with time delay for synergic couples in this manuscript. The quantitative analysis of the model has been done where the asymptotic stability of the equilibrium points of the model have been analyzed. Under the impact of time delay, the Hopf bifurcation analysis of the model has been done. The stability analysis of the model has been studied with the reproduction number less than or greater than 1. By using Laplace transformation, the analysis of the model has been done. The analysis shows that the fractional order model with a time delay can sufficiently improve the components and invigorate the outcomes for either stable or unstable criteria. In this model, all unstable cases are converted to stable cases under neighbourhood points. For all parameters, the reproduction ranges have been described. Finally, to illustrate our derived results numerical simulations have been carried out by using MATLAB. Under the theoretical outcomes from parameter estimation, the love dynamical system is verified.

DYNAMICAL ANALYSIS OF FRACTIONAL ORDER ZIKV MODEL

2021 ◽  
Vol 10 (5) ◽  
pp. 2469-2481
Author(s):  
N.A. Hidayati ◽  
A. Suryanto ◽  
W.M. Kusumawinahyu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Analysis ◽  
Stability Conditions ◽  
Order Model ◽  
Fractional Order Model ◽  
The Stability ◽  
S Model

The ZIKV model presented in this article is developed by modifying \cite{Bonyah2016}’s model. The classical order is changed into fractional order model. The equilibrium points of the model are determined and the stability conditions of each equilibrium point have been done using Routh-Hurwitz conditions. Numerical simulation is presented to verify the result of stability analysis result. Numerical simulation is also used to shows the effect of the order $\alpha$ to the stability of the model’s equilibrium point.

scholarly journals A Fractional-Order Model for HIV Dynamics in a Two-Sex Population

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Fatmawati ◽  
Endrik Mifta Shaiful ◽  
Mohammad Imam Utoyo
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Numerical Approach ◽  
Hiv And Aids ◽  
Order Model ◽  
Fractional Order Model ◽  
Severe Stage ◽  
The Stability ◽  
Immunodeficiency Syndrome ◽  
Predictor Corrector

Human Immunodeficiency Virus (HIV) is a virus that attacks or infects cells in the immune system that causes immune decline. Acquired Immunodeficiency Syndrome (AIDS) is the most severe stage of HIV infection. AIDS is the rapidly spreading and becoming epidemic diseases in the world of almost complete influence across the country. A mathematical model approach of HIV/AIDS dynamic is needed to predict the spread of the diseases in the future. In this paper, we presented a fractional-order model of the spread of HIV and AIDS diseases which incorporates two-sex population. The fractional derivative order of the model is in the interval (0,1]. We compute the basic reproduction number and prove the stability of the equilibriums of the model. The sensitivity analysis also is done to determine the important factor controlling the spread. Using the Adams-type predictor-corrector method, we then perform some numerical simulations for variation values of the order of the fractional derivative. Finally, the effects of various antiretroviral therapy (ART) treatments are studied and compared with numerical approach.

scholarly journals The influence of an infectious disease on a prey-predator model equipped with a fractional-order derivative

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Salih Djilali ◽  
Behzad Ghanbari
Keyword(s):  
Infectious Disease ◽  
Fractional Order ◽  
Graphical Representation ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Hunting Behavior ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Interaction ◽  
The Stability

AbstractIn this research, we discuss the influence of an infectious disease in the evolution of ecological species. A computational predator-prey model of fractional order is considered. Also, we assume that there is a non-fatal infectious disease developed in the prey population. Indeed, it is considered that the predators have a cooperative hunting. This situation occurs when a pair or group of animals coordinate their activities as part of their hunting behavior in order to improve their chances of making a kill and feeding. In this model, we then shift the role of standard derivatives to fractional-order derivatives to take advantage of the valuable benefits of this class of derivatives. Moreover, the stability of equilibrium points is studied. The influence of this infection measured by the transmission rate on the evolution of predator-prey interaction is determined. Many scenarios are obtained, which implies the richness of the suggested model and the importance of this study. The graphical representation of the mathematical results is provided through a precise numerical scheme. This technique enables us to approximate other related models including fractional-derivative operators with high accuracy and efficiency.

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