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IMSP schemes for spatially explicit models of cyclic populations and metapopulation dynamics

Diele, Fasma and Marangi, Carmela and Ragni, Stefania (2014) IMSP schemes for spatially explicit models of cyclic populations and metapopulation dynamics. Mathematics and computers in simulation, Vol. 100 , p. 41-53. ISSN 0378-4754. eISSN 1872-7166. Article.

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DOI: 10.1016/j.matcom.2014.01.006

Abstract

We examine spatially explicit models described by reaction-diffusion partial differential equations for the study of predator–prey population dynamics. The numerical methods we propose are based on the coupling of a finite difference/element spatial discretization and a suitable partitioned Runge–Kutta scheme for the approximation in time. The RK scheme here implemented uses an implicit scheme for the stiff diffusive term and a partitioned RK symplectic scheme for the reaction term (IMSP scheme). We revisit some results provided in literature for the classical Lotka–Volterra system and the Rosenzweig–MacArthur model. We then extend the approach to metapopulation dynamics in order to numerically investigate the effect of migration through a corridor connecting two habitat patches. Moreover, we analyze the synchronization properties of subpopulation dynamics, when the migration occurs through corridors of variable size.

Item Type:Article
ID Code:9765
Status:Published
Refereed:Yes
Uncontrolled Keywords:Predator–prey dynamics, Runge–Kutta schemes, poisson integrators
Subjects:Area 13 - Scienze economiche e statistiche > SECS-S/06 Metodi matematici dell'economia e delle scienze attuariali e finanziarie
Divisions:001 Università di Sassari > 01-a Nuovi Dipartimenti dal 2012 > Scienze economiche e aziendali
Publisher:Elsevier Science
ISSN:0378-4754
eISSN:1872-7166
Copyright Holders:© 2014 IMACS. Published by Elsevier B.V.
Deposited On:28 Apr 2014 11:18

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