Invariant manifold of variable stability in the Koper model

Abstract

The Koper model is a vector field that was developed to study electrochemical oscillations arising in diffusion processes. In the framework of this paper, we consider the Koper model of chemical reactors. It is a three-dimensional autonomous slow-fast system with a folded node and a supercritical singular Hopf bifurcation. The aim is to construct the expansion of invariant manifold with variable stability and corresponding gluing function using the flow curvature method. We show that Koper model has sufficiently smooth invariant surface, called black swan. Computer simulation and computer algebra methods are used for the quantitative analysis of the model.

Modeling Critical Phenomena in a Generalized Van Der Pol Model

“…Фактически, такие поверхности целиком состоят из траекторий-уток, каждая из которых моделирует критическое, но при этом безопасное протекание некоторого процесса. Подобный подход к моделированию критических явлений был впервые применен в работе [8], а затем многократно использован в работах [9][10][11].…”

Slow Manifolds for Stochastic Koper Models with Stable Lévy Noises

“…The Koper model [1] is an idealized model of the chemical reaction described in [2]. Invariant manifolds are useful in investigating the dynamical behavior of the multiscale systems [3,4].…”

“…The existence of a slow manifold for nonlocal fast-slow stochastic evolutionary equations is proved in [21,22]. An invariant manifold of variable stability in the Koper model is established in [2]. It continues to be an active topic on the characterization of a stochastic Koper model driven by the Lévy process for both theoretical reasons and applications.…”