Positive symplectic integrators for predator-prey dynamics
type: Item
instance of: scholarly article
title: Positive symplectic integrators for predator-prey dynamics
zbMATH Open document ID: 1407.37112
author: Fasma Diele
author: Carmela Marangi
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2018-09-05T00:00:00Z
review text: The authors use the analogy between M-systems and Poisson systems in order to construct numerical integration schemes. The rationale behind the generation of these schemes is to transform the original Poisson system into the equivalent Hamiltonian system obtained via the log transform. Then the symplectic Euler scheme is applied to the transformed system and finally the transformed values in terms of the original variables are obtained by inverse transforming the solution via exp transform. This approach is generalized to approximate general predator-prey dynamics.This approach retains the positivity even in the transient phase.
reviewed by: Vasile Marinca
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37J10
Mathematics Subject Classification ID: 37N25
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 6932240
zbMATH Keywords: numerical integration
zbMATH Keywords: symplectic integrators
zbMATH Keywords: Poisson systems
zbMATH Keywords: predator-prey dynamics
describes a project that uses: PRED_PREY
MaRDI profile type: Publication
full work available at URL: dcdsb.2017185
OpenAlex ID: W2741865542
cites work: On the positivity of Poisson integrators for the Lotka-Volterra equations
cites work: Splitting methods for non-autonomous separable dynamical systems
cites work: Optimized high-order splitting methods for some classes of parabolic equations
cites work: Splitting and composition methods for explicit time dependence in separable dynamical systems
cites work: Error Estimates for Polynomial Krylov Approximations to Matrix Functions
cites work: IMSP schemes for spatially explicit models of cyclic populations and metapopulation dynamics
cites work: Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 1: Dirichlet Boundary Conditions
cites work: Overcoming Order Reduction in Diffusion-Reaction Splitting. Part 2: Oblique Boundary Conditions
cites work: Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in MATLAB
cites work: Finite element approximation of spatially extended predator-prey interactions with the Holling type II functional response
cites work: Geometric Numerical Integration
cites work: A second-order positivity preserving scheme for semilinear parabolic problems
cites work: IMEX Runge-Kutta schemes for reaction-diffusion equations
cites work: On the dynamics of a generalized predator-prey system with \(\mathrm{Z}\)-type control
cites work: Spatiotemporal Complexity of Plankton and Fish Dynamics
cites work: Q4625270
cites work: The development of travelling waves in a simple isothermal chemical system - I. Quadratic autocatalysis with linear decay
cites work: Q4238906
cites work: On Positivity Preservation in Some Finite Element Methods for the Heat Equation
cites work: Finite‐difference methods for solving the reaction‐diffusion equations of a simple isothermal chemical system
DOI: 10.3934/DCDSB.2017185
description: scientific article; zbMATH DE number 6932240