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Geometric Numerical Integration in Ecological Modelling

Author

Listed:
  • Fasma Diele

    (Istituto per Applicazioni del Calcolo M.Picone, via Amendola 122/D, 70126 Bari, Italy)

  • Carmela Marangi

    (Istituto per Applicazioni del Calcolo M.Picone, via Amendola 122/D, 70126 Bari, Italy)

Abstract

A major neglected weakness of many ecological models is the numerical method used to solve the governing systems of differential equations. Indeed, the discrete dynamics described by numerical integrators can provide spurious solution of the corresponding continuous model. The approach represented by the geometric numerical integration, by preserving qualitative properties of the solution, leads to improved numerical behaviour expecially in the long-time integration. Positivity of the phase space, Poisson structure of the flows, conservation of invariants that characterize the continuous ecological models are some of the qualitative characteristics well reproduced by geometric numerical integrators. In this paper we review the benefits induced by the use of geometric numerical integrators for some ecological differential models.

Suggested Citation

  • Fasma Diele & Carmela Marangi, 2019. "Geometric Numerical Integration in Ecological Modelling," Mathematics, MDPI, vol. 8(1), pages 1-30, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:25-:d:300500
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    References listed on IDEAS

    as
    1. Pace, Brigida & Diele, Fasma & Marangi, Carmela, 2015. "Splitting schemes and energy preservation for separable Hamiltonian systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 110(C), pages 40-52.
    2. Diele, F. & Marangi, C. & Ragni, S., 2011. "Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1057-1067.
    3. Tousheng Huang & Huayong Zhang & Xuebing Cong & Ge Pan & Xiumin Zhang & Zhao Liu, 2019. "Exploring Spatiotemporal Complexity of a Predator-Prey System with Migration and Diffusion by a Three-Chain Coupled Map Lattice," Complexity, Hindawi, vol. 2019, pages 1-19, May.
    4. Lacitignola, Deborah & Diele, Fasma & Marangi, Carmela, 2015. "Dynamical scenarios from a two-patch predator–prey system with human control – Implications for the conservation of the wolf in the Alta Murgia National Park," Ecological Modelling, Elsevier, vol. 316(C), pages 28-40.
    5. Jef Huisman & Nga N. Pham Thi & David M. Karl & Ben Sommeijer, 2006. "Reduced mixing generates oscillations and chaos in the oceanic deep chlorophyll maximum," Nature, Nature, vol. 439(7074), pages 322-325, January.
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