Expanding the Applicability of the Competitive Modes Conjecture

Sudipto Choudhury; Huibert Reijm; Cornelis Vuik

doi:10.1007/978-3-030-53006-8_3

Expanding the Applicability of the Competitive Modes Conjecture

Sudipto Choudhury, Huibert Reijm, Cornelis Vuik

Numerical Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

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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 language	English
Title of host publication	Nonlinear Dynamics of Discrete and Continuous Systems
Editors	A.K. Abramian, I.V. Andrianov, V.A. Gaiko
Place of Publication	Cham
Publisher	Springer
Pages	31-43
Number of pages	13
ISBN (Electronic)	978-3-030-53006-8
ISBN (Print)	978-3-030-53005-1
DOIs	https://doi.org/10.1007/978-3-030-53006-8_3
Publication status	Published - 2021

Publication series

Name	Advanced Structured Materials
Volume	139
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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10.1007/978-3-030-53006-8_3

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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.",

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Expanding the Applicability of the Competitive Modes Conjecture. / Choudhury, Sudipto; Reijm, Huibert; Vuik, Cornelis.
Nonlinear Dynamics of Discrete and Continuous Systems. ed. / A.K. Abramian; I.V. Andrianov; V.A. Gaiko. Cham: Springer, 2021. p. 31-43 (Advanced Structured Materials; Vol. 139).

Research output: Chapter in Book/Conference proceedings/Edited volume › Chapter › Scientific › peer-review

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Expanding the Applicability of the Competitive Modes Conjecture

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