Bulletin of Mathematical Biology

, Volume 58, Issue 6, pp 1023–1046 | Cite as

Numerical simulation of collapsible-tube flows with sinusoidal forced oscillations

  • J. She
  • C. D. Bertram


Collapsible-tube flow with self-excited oscillations has been extensively investigated. Though physiologically relevant, forced oscillation coupled with self-excited oscillation has received little attention in this context. Based on an ODE model of collapsible-tube flow, the present study applies modern dynamics methods to investigate numerically the responses of forced oscillation to a limit-cycle oscillation which has topological characteristics discovered in previous unforced experiments. A devil's staircase and period-doubling cascades are presented with forcing frequency and amplitude as control parameters. In both cases, details are provided in a bifurcation diagram. Poincaré sections, a frequency spectrum and the largest Lyapunov exponents verify the existence of chaos in some circumstances. The thin fractal structure found in the strange attractors is believed to be a result of high damping and low stiffness in such systems.


Bifurcation Diagram Chaotic Oscillation Force Frequency Large Lyapunov Exponent Ordinary Differential Equation Model 
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Copyright information

© Society for Mathematical Biology 1996

Authors and Affiliations

  • J. She
    • 1
  • C. D. Bertram
    • 1
  1. 1.Graduate School of Biomedical EngineeringUniversity of New South WalesSydneyAustralia

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