On the Extinction–Free Stabilization of Predator-Prey Dynamics

Authors

Stefano Massaroli, Federico Califano, Angela Faragasso, Atsushi Yamashita, Hajime Asama

Abstract

Scientists have long been attracted to mechanisms surrounding the predator–prey system. The Lotka–Volterra (LV) model is the most popular formalism used to investigate the dynamics of this system. LV equations present non-linear dynamics that exhibit periodic oscillations in both prey and predator populations. In practical situations, it is useful to stabilise the system asymptotically to a desired set point (population) wherein the two species coexist by fashioning specific control actions. This control strategy can be beneficial for problems that can arise when there is a risk of extinction of one of the species and human intervention must be planned. One natural and well-established theory for describing systems obeying energy balance laws is the port-Hamiltonian modeling, an extension of classical Hamiltonian mechanics to systems endowed with control and observation. The LV model can be formally represented as a non-linear mechanical oscillator employing the canonical equations of Hamilton. This special mathematical structure aids planning and designing efficient control actions. The proposed strategy employs a systematic procedure to efficiently plan biological control actions and bypass species extinction through asymptotic stabilisation of populations.

Citation

• Journal: IEEE Control Systems Letters
• Year: 2020
• Volume: 4
• Issue: 4
• Pages: 964–969
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/lcsys.2020.2997741

BibTeX

@article{Massaroli_2020,
  title={{On the Extinction–Free Stabilization of Predator-Prey Dynamics}},
  volume={4},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2020.2997741},
  number={4},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Massaroli, Stefano and Califano, Federico and Faragasso, Angela and Yamashita, Atsushi and Asama, Hajime},
  year={2020},
  pages={964--969}
}

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