TY - JOUR
T1 - Three-dimensional forced-damped dynamical systems with rich dynamics
T2 - bifurcations, chaos and unbounded solutions
AU - Miyaji, Tomoyuki
AU - Okamoto, Hisashi
AU - Craik, Alexander Duncan Davidson
N1 - T.M. is supported by the Grant-in-Aid for JSPS Fellow No. 24·5312. H.O. is
partially supported by JSPS KAKENHI 24244007.
PY - 2015
Y1 - 2015
N2 - 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.
AB - 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.
KW - Three-dimensional dynamical system
KW - Period-doubling cascades to chaos
KW - Asymptotic analysis
KW - Lyapunov function
U2 - 10.1016/j.physd.2015.09.001
DO - 10.1016/j.physd.2015.09.001
M3 - Article
SN - 0167-2789
VL - In press
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -