A new approach of asymmetric homoclinic and heteroclinic orbits construction in several typical systems based on the undetermined Padé approximation method
type: Item
instance of: scholarly article
title: A new approach of asymmetric homoclinic and heteroclinic orbits construction in several typical systems based on the undetermined Padé approximation method
zbMATH Open document ID: 1400.34068
DOI: 10.1155/2016/8585290
author: Jing-Jing Feng
author: Wei Wang
author: Shuying Hao
author: Q. C. Zhang
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: In dynamic systems, some nonlinearities generate special connection problems of non-Z\(_{2}\) symmetric homoclinic and heteroclinic orbits. Such orbits are important for analyzing problems of global bifurcation and chaos. In this paper, a general analytical method, based on the undetermined Padé approximation method, is proposed to construct non-Z\(_{2}\) symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z\(_{2}\) heteroclinic orbits are analyzed in detail. An undetermined frequency coefficient and a corresponding new analytic expression are introduced to improve the accuracy of the orbit trajectory. The proposed method shows high precision results for the Nagumo system (one single orbit); general types of non-Z\(_{2}\) symmetric nonlinear quintic systems (orbit with one cusp); and Z\(_{2}\) symmetric system with high-order nonlinear terms (orbit with two cusps). Finally, numerical simulations are used to verify the techniques and demonstrate the enhanced efficiency and precision of the proposed method.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65P40
zbMATH DE Number: 6953682
Wikidata QID: Q59140954
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/8585290
OpenAlex ID: W2480824205
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description: scientific article; zbMATH DE number 6953682