Three-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions
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We consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.
Miyaji , T , Okamoto , H & Craik , A D D 2015 , ' Three-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions ' Physica D: Nonlinear Phenomena , vol In press . DOI: 10.1016/j.physd.2015.09.001
Physica D: Nonlinear Phenomena
Copyright © 2015 Published by Elsevier B.V. This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://dx.doi.org/10.1016/j.physd.2015.09.001
T.M. is supported by the Grant-in-Aid for JSPS Fellow No. 24·5312. H.O. is partially supported by JSPS KAKENHI 24244007.
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