A Hopf bifurcation with translational invariance has been widely considered as an appropriate model for the appearance of spiral vortices in counter-rotating Taylor-Couette flow. Our experimental work demonstrates that flow conditions close to the axial boundaries are responsible for the type of bifurcation scenario, i.e., either asymmetric pure traveling waves or more complex behavior, such as...

We consider a widely used form of models for ship maneuvering, whose nonlinearities entail continuous but nonsmooth second-order modulus terms. For such bifurcations straight motion are not amenable to standard center manifold reduction and normal forms. Based on recently developed analytical approach, we nevertheless determine the character local when stabilizing course with proportional contr...

Human quiet standing is accompanied by body sway. The amplitude of this body sway is known to be larger than would be predicted from simple noise effects, and sway characteristics are changed by neurological disorders. This large sway is thought to arise from nonlinear control with prolonged periods of no control (intermittent control), and a nonlinear control system of this kind has been predi...

This paper presents a detailed analysis on the dynamics of a ring network with short-cut. We first investigate the absolute synchronization on the basis of Lyapunov stability approach, and then discuss the linear stability of the trivial solution by analyzing the distribution of zeros of the characteristic equation. Based on the equivariant branching lemma, we not only obtain the existence of p...