Expanding the Applicability of the Competitive Modes Conjecture

Sudipto Choudhury, Huibert Reijm, Cornelis Vuik

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Abstract

The Competitive Modes Conjecture is a relatively new approach in the field of Dynamical Systems, aiming to understand chaos in strange attractors using Resonance Theory. Up till now, the Conjecture has only been used to study multipolynomial systems because of their simplicity. As such, the study of non-multipolynomial systems is sparse, filled with ambiguity, and lacks mathematical structure. This paper strives to rectify this dilemma, providing the mathematical background needed to rigorously apply the Competitive Modes Conjecture to a certain set of non-multipolynomial systems. Afterwards, we provide an example of this new theory in the non-multipolynomial Wimol-Banlue Attractor, something that up to this point has not been possible as far as the authors know.

Original languageEnglish
Title of host publicationNonlinear Dynamics of Discrete and Continuous Systems
EditorsA.K. Abramian, I.V. Andrianov, V.A. Gaiko
Place of PublicationCham
PublisherSpringer
Pages31-43
Number of pages13
ISBN (Electronic)978-3-030-53006-8
ISBN (Print)978-3-030-53005-1
DOIs
Publication statusPublished - 2021

Publication series

NameAdvanced Structured Materials
Volume139
ISSN (Print)1869-8433
ISSN (Electronic)1869-8441

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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