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High-order study of the canard explosion in an aircraft ground dynamics model

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Abstract

A planar system has been proposed in the paper Rankin et al. (Nonlinear Dyn 66:681–688, 2011) to understand the canard explosion detected in a 6D aircraft ground dynamics model. A specific feature of this minimal 2D system is a critical manifold with a single fold and an asymptote. In this paper, we provide a high-order analytical prediction (in fact, up to any wanted order) of the canard explosion in this system. Using a nonlinear time transformation method, we are able to approximate not only the critical parameter value, but also the critical manifold in the phase space. The comparison of our theoretical results with the corresponding numerical continuations shows a very good agreement.

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Authors and Affiliations

  1. School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

    Bo-Wei Qin

  2. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong

    Kwok-Wai Chung

  3. Departamento de Ciencias Integradas, Centro de Estudios Avanzados en Física, Matemática y Computación, Universidad de Huelva, 21071, Huelva, Spain

    Antonio Algaba

  4. Departamento de Matemática Aplicada II, E.T.S. Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos s/n, 41092, Sevilla, Spain

    Alejandro J. Rodríguez-Luis

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  1. Bo-Wei Qin
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  3. Antonio Algaba
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  4. Alejandro J. Rodríguez-Luis
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Correspondence to Alejandro J. Rodríguez-Luis.

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We thank the reviewers for their careful reading of the manuscript and their constructive remarks. This work has been partially supported by the Ministerio de Economía y Competitividad (project MTM2017-87915-C2-1-P, co-financed with FEDER funds), by the Ministerio de Ciencia, Innovación y Universidades (project PGC2018-096265-B-I00, co-financed with FEDER funds) and by the Consejería de Economía, Innovación, Ciencia y Empleo de la Junta de Andalucía (FQM-276, TIC-0130, UHU-1260150 and P12-FQM-1658). It has also been supported by the Strategic Research Grant of the City University of Hong Kong (Grant No. 7004848). B.W.Q. is also grateful to the Instituto de Matemáticas de la Universidad de Sevilla (IMUS) and to the Centro de Estudios Avanzados en Física, Matemática y Computación de la Universidad de Huelva (CEAFMC) for collaborating in the financing of his research stays in Seville and Huelva.

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Qin, BW., Chung, KW., Algaba, A. et al. High-order study of the canard explosion in an aircraft ground dynamics model. Nonlinear Dyn 100, 1079–1090 (2020). https://doi.org/10.1007/s11071-020-05575-w

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  • DOI: https://doi.org/10.1007/s11071-020-05575-w

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