Connecting orbits for a singular nonautonomous real Ginzburg-Landau type equation
Daniel Wilczak, Piotr Zgliczy\'nski
TL;DR
This paper introduces a computational method for identifying connecting orbits in nonautonomous singular ODEs, demonstrated on a Ginzburg-Landau type equation related to pattern formation.
Contribution
The paper presents a novel approach for computing stable and unstable sets and connecting orbits in nonautonomous singular differential equations.
Findings
Successfully applied to a Ginzburg-Landau type equation
Identified specific connecting orbits in a singular nonautonomous setting
Enhanced understanding of pattern formation mechanisms
Abstract
We propose a method for computation of stable and unstable sets associated to hyperbolic equilibria of nonautonomous ODEs and for computation of specific type of connecting orbits in nonautonomous singular ODEs. We apply the method to a certain a singular nonautonomous real Ginzburg-Landau type equation, which that arises from the problem of formation of spots in the Swift-Hohenberg equation.
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