Search results for " adaptive control"
showing 2 items of 12 documents
Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System
2012
In this paper a four-dimensional hyperchaotic system with only one equilibrium is considered and its double Hopf bifurcations are investigated. The general post-bifurcation and stability analysis are carried out using the normal form of the system obtained via the method of multiple scales. The dynamics of the orbits predicted through the normal form comprises possible regimes of periodic solutions, two-period tori, and three-period tori in parameter space. Moreover, we show how the hyperchaotic synchronization of this system can be realized via an adaptive control scheme. Numerical simulations are included to show the effectiveness of the designed control.
Analysis and control of a seven mode truncation of the Kolmogorov flow with drag.
2008
The transition from laminar to chaotic motion in a viscous fluid flow is investigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov flow with drag friction. Analytical expressions of the bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynoplds number is increased for fixed values of the drag parameter. An adaptive stabilization of the system trajectories to an equilibrium point or to a periodic orbit is obtained through a model reference approach which makes the control global.