Attractor as a convex combination of a set of attractors
Danca, Marius-F.; Fĕckan, Michal; Kuznetsov, Nikolay; Chen, Guanrong (2021). Attractor as a convex combination of a set of attractors. Communications in Nonlinear Science and Numerical Simulation, 96, 105721. DOI: 10.1016/j.cnsns.2021.105721
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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.