Math. Model. Nat. Phenom.
Volume 14, Number 4, 2019
Singular perturbations and multiscale systems
|Number of page(s)||12|
|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,
** Corresponding author: firstname.lastname@example.org
Accepted: 29 April 2019
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
© EDP Sciences, 2019
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