COMPUTATION OF CONNECTION MATRICES USING THE SOFTWARE PACKAGE conley

Author:

BARAKAT MOHAMED1,MAIER-PAAPE STANISLAUS2

Affiliation:

1. Lehrstuhl B für Mathematik, RWTH-Aachen University, 52062 Aachen, Germany

2. Institut für Mathematik, RWTH-Aachen University, 52062 Aachen, Germany

Abstract

In this paper we demonstrate the power of the computer algebra package conley, which enables one to compute connection and transition matrices, two of the main algebraic tools of the CONLEY index theory. In particular, we study the CAHN–HILLIARD equation on the unit square and extend the results obtained in [Maier-Paape et al., 2007] to a bigger range of the bifurcation parameter. Besides providing several explicit computations using conley, the definition of connection matrices is reconsidered, simplified, and presented in a self-contained manner in the language of CONLEY index theory. Furthermore, we introduce so-called energy induced bifurcation intervals, which can be utilized by conley to differential equations with a parameter. These bifurcation intervals are used to automatically path-follow the set of connection matrices at bifurcation points of the underlying set of equilibria.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A computational framework for connection matrix theory;Journal of Applied and Computational Topology;2021-05-31

2. Generalized topological transition matrix;Topological Methods in Nonlinear Analysis;2016-09-02

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