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The diffusive Lotka-Volterra predator-prey system with delay

Journal Article


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Abstract


  • Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations. This approach is used to obtain a lower-order, ordinary differential delay equation model for the system of governing delay partial differential equations. Steady-state and transient solutions and the region of parameter space, in which Hopf bifurcations occur, are all found. In some cases simple linear expressions are found as approximations, to describe steady-state solutions and the Hopf parameter regions. An asymptotic analysis for the periodic solution near the Hopf bifurcation point is performed for the one-dimensional domain. An excellent agreement is shown in comparisons between semi-analytical and numerical solutions of the governing equations.

Publication Date


  • 2015

Citation


  • Al Noufaey, K. S., Marchant, T. R. & Edwards, M. P. (2015). The diffusive Lotka-Volterra predator-prey system with delay. Mathematical Biosciences, 270 30-40.

Scopus Eid


  • 2-s2.0-84947586074

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6027&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5000

Number Of Pages


  • 10

Start Page


  • 30

End Page


  • 40

Volume


  • 270

Abstract


  • Semi-analytical solutions for the diffusive Lotka-Volterra predator-prey system with delay are considered in one and two-dimensional domains. The Galerkin method is applied, which approximates the spatial structure of both the predator and prey populations. This approach is used to obtain a lower-order, ordinary differential delay equation model for the system of governing delay partial differential equations. Steady-state and transient solutions and the region of parameter space, in which Hopf bifurcations occur, are all found. In some cases simple linear expressions are found as approximations, to describe steady-state solutions and the Hopf parameter regions. An asymptotic analysis for the periodic solution near the Hopf bifurcation point is performed for the one-dimensional domain. An excellent agreement is shown in comparisons between semi-analytical and numerical solutions of the governing equations.

Publication Date


  • 2015

Citation


  • Al Noufaey, K. S., Marchant, T. R. & Edwards, M. P. (2015). The diffusive Lotka-Volterra predator-prey system with delay. Mathematical Biosciences, 270 30-40.

Scopus Eid


  • 2-s2.0-84947586074

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=6027&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/5000

Number Of Pages


  • 10

Start Page


  • 30

End Page


  • 40

Volume


  • 270