English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In dynamic systems, some nonlinearities generate special connection problems of non-Z2 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-Z2 symmetric homoclinic and heteroclinic orbits which are affected by nonlinearity factors. Geometric and symmetrical characteristics of non-Z2 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-Z2 symmetric nonlinear quintic systems (orbit with one cusp); and Z2 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

mathematical problems in engineering

A New Approach of Asymmetric Homoclinic and Heteroclinic Orbits Construction in Several Typical Systems Based on the Undetermined Padé Approximation Method