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Separatrix reconstruction to identify tipping points in an eco-epidemiological model

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  • Francomano, Elisa
  • Hilker, Frank M.
  • Paliaga, Marta
  • Venturino, Ezio

Abstract

Many ecological systems exhibit tipping points such that they suddenly shift from one state to another. These shifts can be devastating from an ecological point of view, and additionally have severe implications for the socio-economic system. They can be caused by overcritical perturbations of the state variables such as external shocks, disease emergence, or species removal. It is therefore important to be able to quantify the tipping points. Here we present a study of the tipping points by considering the basins of attraction of the stable equilibrium points. We address the question of finding the tipping points that lie on the separatrix surface, which partitions the space of system trajectories. We present an algorithm that reconstructs the separatrix by using a Moving Least Squares approximant based on radial basis functions. The algorithm is applied to an eco-epidemiological model of pack hunting predators that suffer disease infection. Our analysis reveals that strong hunting cooperation considerably promotes the survival of predators and renders the predators resilient to perturbations.

Suggested Citation

  • Francomano, Elisa & Hilker, Frank M. & Paliaga, Marta & Venturino, Ezio, 2018. "Separatrix reconstruction to identify tipping points in an eco-epidemiological model," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 80-91.
    • Handle: RePEc:eee:apmaco:v:318:y:2018:i:c:p:80-91
    DOI: 10.1016/j.amc.2017.07.022
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    References listed on IDEAS

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    1. Joldes, Grand Roman & Chowdhury, Habibullah Amin & Wittek, Adam & Doyle, Barry & Miller, Karol, 2015. "Modified moving least squares with polynomial bases for scattered data approximation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 893-902.
    2. Ala, Guido & Fasshauer, Gregory E. & Francomano, Elisa & Ganci, Salvatore & McCourt, Michael J., 2017. "An augmented MFS approach for brain activity reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 3-15.
    3. Peter J. Mumby & Alan Hastings & Helen J. Edwards, 2007. "Thresholds and the resilience of Caribbean coral reefs," Nature, Nature, vol. 450(7166), pages 98-101, November.
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    Cited by:

    1. Gabrick, Enrique C. & Sayari, Elaheh & Protachevicz, Paulo R. & Szezech, José D. & Iarosz, Kelly C. & de Souza, Silvio L.T. & Almeida, Alexandre C.L. & Viana, Ricardo L. & Caldas, Iberê L. & Batista, , 2023. "Unpredictability in seasonal infectious diseases spread," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Francomano, Elisa & Paliaga, Marta, 2020. "A normalized iterative Smoothed Particle Hydrodynamics method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 171-180.
    3. Francomano, E. & Paliaga, M., 2018. "Highlighting numerical insights of an efficient SPH method," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 899-915.
    4. Farzad Fatehi & Yuliya N. Kyrychko & Konstantin B. Blyuss, 2018. "Effects of Viral and Cytokine Delays on Dynamics of Autoimmunity," Mathematics, MDPI, vol. 6(5), pages 1-24, April.
    5. Antonelli, L. & Francomano, E. & Gregoretti, F., 2021. "A CUDA-based implementation of an improved SPH method on GPU," Applied Mathematics and Computation, Elsevier, vol. 409(C).

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