Math. Model. Nat. Phenom.
Volume 17, 2022
|Number of page(s)
|30 August 2022
Stochastic bifurcations and tipping phenomena of insect outbreak systems driven by α-stable Lévy processes
Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
2 School of Automation, Nanjing University of Science and Technology, Nanjing 210094, China
3 School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China
* Corresponding author: firstname.lastname@example.org
Accepted: 2 August 2022
In this work, we mainly characterize stochastic bifurcations and tipping phenomena of insect outbreak dynamical systems driven by α-stable Lévy processes. In one-dimensional insect outbreak model, we find the fixed points representing refuge and outbreak from the bifurcation curves, and carry out a sensitivity analysis with respect to small changes in the model parameters, the stability index and the noise intensity. We perform the numerical simulations of dynamical trajectories using Monte Carlo methods, which contribute to looking at stochastic hysteresis phenomenon. As for two-dimensional insect outbreak system, we identify the global stability properties of fixed points and express the probability density function by the stationary solution of the nonlocal Fokker-Planck equation. Through numerical modelling, the phase portrait makes it possible to detect critical transitions among the stable states. It is then worth describing stochastic bifurcation associated with tipping points induced by noise through a careful examination of the dynamical paths of the insect outbreak system with external forcing. The results give new insight into the sensitivity of ecosystems to realistic environmental changes represented by stochastic perturbations.
Mathematics Subject Classification: 37H20 / 60G65
Key words: Insect outbreak systems / stochastic bifurcations / tipping phenomena / environmental changes / Lévy noises
© The authors. Published by EDP Sciences, 2022
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