In this work, the onset and growth of the spinning instability is analyzed for an isothermal Newtonian liquid by examining the nonlinear dynamics of the most unstable spatial mode.
We are particularly interested in the attracting case in which case we call these invariant sets heteroclinic attractors and trajectories approaching such attractors show a typical intermittent behaviour periods that are close to the dynamics of an unstable saddle-type invariant set, and switches between different behaviours.
The PLL dynamics in the unstable region is found to have a sequence of period doubling bifurcation and chaos.
A numerical simulation involving the roll dynamics of an unstable aircraft, whose aerodynamic coefficients are unknown, illustrates our theoretical framework.
He can say that because the science is now done on the fundamentally unstable dynamics of the Earth's geophysical system.
The solution is examined by means of numerical simulations performed within the three regions of the flow velocity: low subcritical, where the Coriolis acceleration of the conveyed fluid generates the predominate damping force; high subcritical, where the inertia of the fluid begins to dominate the dynamics of the system; and low supercritical, where unstable flutter vibrations start to arise.
2, we know that when (tau< tau_{0}), a stable fixed point takes place in the N P state space, and that when (taugetau_{0}), the fixed point turns to be unstable and the dynamics of the discrete system is attracted to an invariant closed curve.
In Fig. 4, we give the dynamics of the waves for parameter values that support unstable waves (points marked II and I in Fig. 3a,c respectively).
Since the output data from the unstable system does not show enough information or dynamics of the system.
Moreover a novel robustness analysis of the unstable case is presented to demonstrate the limitations imposed by the unstable dynamics and the dead time.
