Fractional-order delayed predator–prey systems with Holling type-II functional response

F. A. Rihan; S. Lakshmanan; A. H. Hashish; R. Rakkiyappan; E. Ahmed

doi:10.1007/s11071-015-1905-8

Fractional-order delayed predator–prey systems with Holling type-II functional response

F. A. Rihan, S. Lakshmanan, A. H. Hashish, R. Rakkiyappan, E. Ahmed

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

163 Citations (Scopus)

Abstract

In this paper, a fractional dynamical system of predator–prey with Holling type-II functional response and time delay is studied. Local and global stability of existence steady states and Hopf bifurcation with respect to the delay is investigated, with fractional-order (Formula presented). It is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Unconditionally, stable implicit scheme for the numerical simulations of the fractional-order delay differential model is introduced. The numerical simulations show the effectiveness of the numerical method and confirm the theoretical results. The presence of fractional order in the delayed differential model improves the stability of the solutions and enrich the dynamics of the model.

Original language	English
Pages (from-to)	777-789
Number of pages	13
Journal	Nonlinear Dynamics
Volume	80
Issue number	1-2
DOIs	https://doi.org/10.1007/s11071-015-1905-8
Publication status	Published - Apr 2015

Keywords

Fractional calculus
Hopf bifurcation
Predator–prey
Stability
Time delay

ASJC Scopus subject areas

Control and Systems Engineering
Aerospace Engineering
Ocean Engineering
Mechanical Engineering
Applied Mathematics
Electrical and Electronic Engineering

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10.1007/s11071-015-1905-8

Cite this

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title = "Fractional-order delayed predator–prey systems with Holling type-II functional response",

abstract = "In this paper, a fractional dynamical system of predator–prey with Holling type-II functional response and time delay is studied. Local and global stability of existence steady states and Hopf bifurcation with respect to the delay is investigated, with fractional-order (Formula presented). It is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Unconditionally, stable implicit scheme for the numerical simulations of the fractional-order delay differential model is introduced. The numerical simulations show the effectiveness of the numerical method and confirm the theoretical results. The presence of fractional order in the delayed differential model improves the stability of the solutions and enrich the dynamics of the model.",

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T1 - Fractional-order delayed predator–prey systems with Holling type-II functional response

AU - Rihan, F. A.

AU - Lakshmanan, S.

AU - Hashish, A. H.

AU - Rakkiyappan, R.

AU - Ahmed, E.

PY - 2015/4

Y1 - 2015/4

N2 - In this paper, a fractional dynamical system of predator–prey with Holling type-II functional response and time delay is studied. Local and global stability of existence steady states and Hopf bifurcation with respect to the delay is investigated, with fractional-order (Formula presented). It is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Unconditionally, stable implicit scheme for the numerical simulations of the fractional-order delay differential model is introduced. The numerical simulations show the effectiveness of the numerical method and confirm the theoretical results. The presence of fractional order in the delayed differential model improves the stability of the solutions and enrich the dynamics of the model.

AB - In this paper, a fractional dynamical system of predator–prey with Holling type-II functional response and time delay is studied. Local and global stability of existence steady states and Hopf bifurcation with respect to the delay is investigated, with fractional-order (Formula presented). It is found that Hopf bifurcation occurs when the delay passes through a sequence of critical values. Unconditionally, stable implicit scheme for the numerical simulations of the fractional-order delay differential model is introduced. The numerical simulations show the effectiveness of the numerical method and confirm the theoretical results. The presence of fractional order in the delayed differential model improves the stability of the solutions and enrich the dynamics of the model.

KW - Fractional calculus

KW - Hopf bifurcation

KW - Predator–prey

KW - Stability

KW - Time delay

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Fractional-order delayed predator–prey systems with Holling type-II functional response

Abstract

Keywords

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