A novel model of dipteran flight mechanism

Qingjie Cao*, Yeping Xiong, Marian Wiercigroch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Citations (Scopus)


In this paper, a novel model for the mechanism of dipteran flight motor is proposed and a flight dynamics is explored by nonlinear dynamics techniques. This model comprises a lumped mass, a pair of inclined rigid bars and a pair of horizontal springs. Even the springs are linear, this system is irrationally nonlinear which causes difficulty for classical nonlinear analysis. We investigate the original irrational equation by direct numerical simulation avoiding Taylor’s expansion to retain the intrinsic character of dipteran flight. This enables us to reveal the bounded characteristics of depteran flight including “click”, bursting and the “complex” flight patterns. Equilibrium analysis demonstrates the “click” mechanism and the “non-click” condition for the unperturbed system. While for the perturbed system, Poincaré section and basin analysis are carried out to demonstrate the bursting behaviour, transitions between different flight modes and their coexistence. The results obtained herein reveal that the complex bifurcations of equilibria, periodic behaviours and the chaotic motions of the presented system associate respectively with “resting”, “calm” and “complex” flight. All the results related to the perturbed system are obtained by the fourth order Runge–Kutta method which ensures the accuracy of the computation. This study provides an additional insight into the understanding of various flight dynamics of insects and bridges a gap between the nonlinear dynamics and the biology.

Original languageEnglish
Pages (from-to)1-11
Number of pages11
JournalInternational Journal of Dynamics and Control
Issue number1
Early online date13 Mar 2013
Publication statusPublished - Mar 2013

Bibliographical note

The first author acknowledges the financial support of National Science Foundation of China under the grants of 10872136 and 11072065. The financial support from Royal Academy of Engineering Research Exchanging with China and India is greatly appreciated by Y.P. Xiong and Q. Cao.


  • Bounded flight
  • Dipteran flight
  • Irrational nonlinearity
  • Multiple flight patterns
  • Nonlinear dynamics
  • “Click” mechanism


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