We try to stabilize equilibrium solutions of physical models described by a class of coupled first-order linear partial differential equations with nonlinear boundary conditions.
This entire period or the 'cycle of erosion' can be divided into three stages, viz., monandnock (old) (H si 0.3), in which the watershed is fully stabilized; equilibrium or mature stage (0.3 H si 0.6); and inequilibrium or young stage (H si 0.6), in which the watershed is highly susceptible to erosion (Strahler 1952).
Caused by the synchronization (which is induced by the sorting procedure), the selected cells are predicted to transiently lead to a higher fraction of cells in the opposing state ("over-shooting") as compared to the stabilized equilibrium.
Depending on the magnitude of the assumed background noise (i.e. the size of σ2), this synchronization is lost over time and the stabilized equilibrium between Nanog-high and Nanog-low states is re-established.
When the pendulum is stabilized in the upside-down position, it still experiences small high-frequency oscillations around the stabilized equilibrium point.
The aim of this work is to design an explicit finite dimensional boundary feedback controller for locally exponentially stabilizing the equilibrium solutions to Fisher's equation in both L2 0,1) and H1 0,1).
Thus, the angular position of the wheels (remaining DOF) is driven to steady state, i.e., it is maintained stabilized (static equilibrium) (φ̇= 0rad/s), or at least its velocity (mechanical equilibrium) (φ̇="const.rad/s).rad/s
The problem addressed is to design a feedback regulator that can stabilize an equilibrium of the closed-loop system and, around this equilibrium, to synthesize a required dispersion of random states of the corresponding system.
Within this neighborhood, the control then acts as a high-gain feedback that stabilizes the equilibrium point.
The principle of synchronization is used to globally and exponentially stabilize the equilibrium points of the hyperchaotic system.
