PMID: 8953255Nov 1, 1996Paper

Numerical simulation of collapsible-tube flows with sinusoidal forced oscillations

Bulletin of Mathematical Biology
J She, C D Bertram

Abstract

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.

References

Feb 1, 1992·Journal of Biomechanical Engineering·O E Jensen
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Jul 1, 1996·Bulletin of Mathematical Biology·J P ArmitsteadO E Jensen
Aug 1, 1987·Physical Review A: General Physics·U Parlitz, W Lauterborn

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Citations

Aug 21, 2002·Computer Methods in Biomechanics and Biomedical Engineering·Lynne E Bilston
Feb 27, 2004·Medical Engineering & Physics·C D BertramH U Voss
Sep 12, 2018·Chemical Record : an Official Publication of the Chemical Society of Japan ... [et Al.]·Afsaneh Taheri Kal-Koshvandi, Majid M Heravi
Mar 31, 2009·The Journal of Experimental Biology·Coen P H ElemansJohan L van Leeuwen

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