Attractor as a convex combination of a set of attractors
Danca, M.-F., Fĕckan, M., Kuznetsov, N., & Chen, G. (2021). Attractor as a convex combination of a set of attractors. Communications in Nonlinear Science and Numerical Simulation, 96, Article 105721. https://doi.org/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.
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Additional information about fundingM. Fĕckan is partially supported by the Slovak Research and Development Agency under the Contract No. APVV-18-0308, and the Slovak Grant Agency VEGA No. 1/0358/20 and No. 2/0127/20, N. Kuznetsov, G. Chen and M.-F. Danca are supported by the Russian Science Foundation project 19-41-02002 (Section 2 and dummyTXdummy-( 3).
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