Approximating basins of attraction for dynamical systems via stable radial bases

TL;DR

This paper introduces a method using stable radial bases to approximate basins of attraction in multi-stable dynamical systems, aiding in understanding complex population models.

Contribution

It presents a novel approach to reconstruct basins of attraction through implicit interpolation with stable radial bases, applied to a multi-stable competition model.

Findings

Successfully approximated basins of attraction in a three-stable-equilibrium model

Demonstrated the effectiveness of the method in partitioning phase space

Provided a practical tool for analyzing multi-stability in applied sciences

Abstract

In applied sciences, such as physics and biology, it is often required to model the evolution of populations via dynamical systems. In this paper, we focus on the problem of approximating the basins of attraction of such models in case of multi-stability. We propose to reconstruct the domains of attraction via an implicit interpolant using stable radial bases, obtaining the surfaces by partitioning the phase space into disjoint regions. An application to a competition model presenting jointly three stable equilibria is considered.