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Positive symplectic integrators for predator-prey dynamics

Authors: Fasma Diele; Carmela Marangi;

Positive symplectic integrators for predator-prey dynamics

Abstract

We propose novel positive numerical integrators for approximating predator-prey models. The schemes are based on suitable symplectic procedures applied to the dynamical system written in terms of the log transformation of the original variables. Even if this approach is not new when dealing with Hamiltonian systems, it is of particular interest in population dynamics since the positivity of the approximation is ensured without any restriction on the temporal step size. When applied to separable M-systems, the resulting schemes are proved to be explicit, positive, Poisson maps. The approach is generalized to predator-prey dynamics which do not exhibit an M-system structure and successively to reaction-diffusion equations describing spatially extended dynamics. A classical polynomial Krylov approximation for the diffusive term joint with the proposed schemes for the reaction, allows us to propose numerical schemes which are explicit when applied to well established ecological models for predator-prey dynamics. Numerical simulations show that the considered approach provides results which outperform the numerical approximations found in recent literature.

Country
Italy
Subjects by Vocabulary

Microsoft Academic Graph classification: education.field_of_study Polynomial Population Dynamical system Hamiltonian system Separable space Applied mathematics Symplectic integrator education Variational integrator Mathematics Symplectic geometry

Keywords

Rosenzweig-MacArthur model., Applied Mathematics, predator-prey dynamics, Positive numerical integration, Discrete Mathematics and Combinatorics

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    Top 10%
  • citations
    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    10
    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    Average
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    Top 10%
    Powered byBIP!BIP!
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Found an issue? Give us feedback
citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Top 10%
Average
Top 10%
gold
Funded by
EC| ECOPOTENTIAL
Project
ECOPOTENTIAL
ECOPOTENTIAL: IMPROVING FUTURE ECOSYSTEM BENEFITS THROUGH EARTH OBSERVATIONS
  • Funder: European Commission (EC)
  • Project Code: 641762
  • Funding stream: H2020 | RIA
Validated by funder
Related to Research communities
Sustainable Development Solutions Network - Greece
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