Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators

F. A. Rihan; C. Rajivganthi

doi:10.1016/j.chaos.2020.110365

Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators

F. A. Rihan, C. Rajivganthi

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

42 Citations (Scopus)

Abstract

In this work, we study the dynamics of a fractional-order delay differential model of prey-predator system with Holling-type III and predator population is infected by an infectious disease. We use Laplace transform, Lyapunov functional, and stability criterion to establish new sufficient conditions that ensure the asymptotic stability of the steady states of the system. Existence of Hopf bifurcation is investigated. The model undergoes Hopf bifurcation, when the feedback time-delays passes through the critical values τ₁^*and τ₂^*. Fractional-order improves the dynamics of the model; while time-delays play a considerable influence on the creation of Hopf bifurcation and stability of the system. Some numerical simulations are provided to validate the theoretical results.

Original language	English
Article number	110365
Journal	Chaos, Solitons and Fractals
Volume	141
DOIs	https://doi.org/10.1016/j.chaos.2020.110365
Publication status	Published - Dec 2020

Keywords

Bifurcation
Eco-epidemiological model
Fractional-order
Prey-Predator
Stability
Time-delay

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

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10.1016/j.chaos.2020.110365

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title = "Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators",

abstract = "In this work, we study the dynamics of a fractional-order delay differential model of prey-predator system with Holling-type III and predator population is infected by an infectious disease. We use Laplace transform, Lyapunov functional, and stability criterion to establish new sufficient conditions that ensure the asymptotic stability of the steady states of the system. Existence of Hopf bifurcation is investigated. The model undergoes Hopf bifurcation, when the feedback time-delays passes through the critical values τ1*and τ2*. Fractional-order improves the dynamics of the model; while time-delays play a considerable influence on the creation of Hopf bifurcation and stability of the system. Some numerical simulations are provided to validate the theoretical results.",

keywords = "Bifurcation, Eco-epidemiological model, Fractional-order, Prey-Predator, Stability, Time-delay",

author = "Rihan, {F. A.} and C. Rajivganthi",

note = "Funding Information: This work is supported by UPAR-2021 grant project (Grant Code: G00003440), ( UAE University , UAE). The authors would like to thank the editor and referees for their valuable comments and suggestions, which improved the quality of this manuscript. Funding Information: This work is supported by UPAR-2021 grant project (Grant Code: G00003440), (UAE University, UAE). The authors would like to thank the editor and referees for their valuable comments and suggestions, which improved the quality of this manuscript. Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",

year = "2020",

month = dec,

doi = "10.1016/j.chaos.2020.110365",

language = "English",

volume = "141",

journal = "Chaos, Solitons and Fractals",

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AU - Rihan, F. A.

AU - Rajivganthi, C.

N1 - Funding Information: This work is supported by UPAR-2021 grant project (Grant Code: G00003440), ( UAE University , UAE). The authors would like to thank the editor and referees for their valuable comments and suggestions, which improved the quality of this manuscript. Funding Information: This work is supported by UPAR-2021 grant project (Grant Code: G00003440), (UAE University, UAE). The authors would like to thank the editor and referees for their valuable comments and suggestions, which improved the quality of this manuscript. Publisher Copyright: © 2020 Elsevier Ltd

PY - 2020/12

Y1 - 2020/12

N2 - In this work, we study the dynamics of a fractional-order delay differential model of prey-predator system with Holling-type III and predator population is infected by an infectious disease. We use Laplace transform, Lyapunov functional, and stability criterion to establish new sufficient conditions that ensure the asymptotic stability of the steady states of the system. Existence of Hopf bifurcation is investigated. The model undergoes Hopf bifurcation, when the feedback time-delays passes through the critical values τ1*and τ2*. Fractional-order improves the dynamics of the model; while time-delays play a considerable influence on the creation of Hopf bifurcation and stability of the system. Some numerical simulations are provided to validate the theoretical results.

AB - In this work, we study the dynamics of a fractional-order delay differential model of prey-predator system with Holling-type III and predator population is infected by an infectious disease. We use Laplace transform, Lyapunov functional, and stability criterion to establish new sufficient conditions that ensure the asymptotic stability of the steady states of the system. Existence of Hopf bifurcation is investigated. The model undergoes Hopf bifurcation, when the feedback time-delays passes through the critical values τ1*and τ2*. Fractional-order improves the dynamics of the model; while time-delays play a considerable influence on the creation of Hopf bifurcation and stability of the system. Some numerical simulations are provided to validate the theoretical results.

KW - Bifurcation

KW - Eco-epidemiological model

KW - Fractional-order

KW - Prey-Predator

KW - Stability

KW - Time-delay

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Dynamics of fractional-order delay differential model of prey-predator system with Holling-type III and infection among predators

Abstract

Keywords

ASJC Scopus subject areas

UN SDGs

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