Attractor as a convex combination of a set of attractors

Marius F. Danca, Michal Fĕckan, Nikolay Kuznetsov, Guanrong Chen

Research output: Contribution to journalArticlepeer-review

Abstract

This paper presents an effective approach to constructing numerical attractors of a general class of continuous homogenous dynamical systems: decomposing an attractor as a convex combination of a set of other existing attractors. For this purpose, the convergent Parameter Switching (PS) numerical method is used to integrate the underlying dynamical system. The method is built on a convergent fixed step-size numerical method for ODEs. The paper shows that the PS algorithm, incorporating two binary operations, can be used to approximate any numerical attractor via a convex combination of some existing attractors. Several examples are presented to show the effectiveness of the proposed method.

Original languageEnglish
Article number105721
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume96
DOIs
StatePublished - May 2021

Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Keywords

  • Continuous-time system
  • Numerical attractor
  • Parameter switching

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