| Issue |
Math. Model. Nat. Phenom.
Volume 14, Number 4, 2019
Singular perturbations and multiscale systems
|
|
|---|---|---|
| Article Number | 408 | |
| Number of page(s) | 12 | |
| DOI | https://doi.org/10.1051/mmnp/2019024 | |
| Published online | 07 June 2019 | |
Black swans and canards in two predator – one prey model*
Department of Differential Equations and Control Theory, Samara National Research University,
Samara, Russia.
** Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
28
October
2018
Accepted:
29
April
2019
Abstract
In this paper, we show how canards can be easily caught in a class of 3D systems with an exact black swan (a slow invariant manifold of variable stability). We demonstrate this approach to a canard chase via the two predator – one prey model. It is shown that the technique described allows us to get various 3D oscillations by changing the shape of the trajectories of two 2D-projections of the original 3D system.
Mathematics Subject Classification: 34E17 / 92D25
Key words: Singular perturbation / stability / invariant manifolds / canards / black swans / population dynamics / competition model
This work was funded by RFBR and Samara Region (project 16-41-630529-p) and the Ministry of Education and Science of the Russian Federation under the Competitiveness Enhancement Program of Samara University (2013–2020).
© EDP Sciences, 2019
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