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


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
StatePublished - May 2021

Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics


  • Continuous-time system
  • Numerical attractor
  • Parameter switching


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