Results 281 to 290 of about 306,199 (304)
Some of the next articles are maybe not open access.
2010
This chapter provides a systematic technique for designing center manifold of closed loop of nonlinear systems to stabilize the system. The method was firstly presented in [6]. Section 11.1 introduces some fundamental concepts and results about center manifold theory. Section 11.2 considers the case when the zero dynamics has minimum phase.
Daizhan Cheng, Xiaoming Hu, Tielong Shen
openaire +1 more source
This chapter provides a systematic technique for designing center manifold of closed loop of nonlinear systems to stabilize the system. The method was firstly presented in [6]. Section 11.1 introduces some fundamental concepts and results about center manifold theory. Section 11.2 considers the case when the zero dynamics has minimum phase.
Daizhan Cheng, Xiaoming Hu, Tielong Shen
openaire +1 more source
2000
Center manifold theory is essential for analyzing local bifurcations. As the Liapunov-Schmidt reduction for stationary and Hopf bifurcations, center manifold theory is used to reduce a dynamical system near a nonhyperbolic equilibrium or a periodic solution to a low-dimensional system with the vector field as functions of the critical modes ...
openaire +1 more source
Center manifold theory is essential for analyzing local bifurcations. As the Liapunov-Schmidt reduction for stationary and Hopf bifurcations, center manifold theory is used to reduce a dynamical system near a nonhyperbolic equilibrium or a periodic solution to a low-dimensional system with the vector field as functions of the critical modes ...
openaire +1 more source
One-Dimensional Center Manifolds are C∞
Results in Mathematics, 1992It is well known that center manifolds of analytic differential equations are not of class C∞ in general. In this paper it is shown that they are indeed C∞ if they are one-dimensional.
openaire +2 more sources
Analytic Center Manifolds of Dimension One
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 1986AbstractThe flow of a system of ordinary differential equations near an equilibrium point is completely determined by the flow restricted to a corresponding center manifold. Even for analytic equations center manifolds need not be analytic and therefore, in general, the flow on a center manifold cannot be described by an analytic equation.
openaire +1 more source
Numerical Center Manifold Methods
2017This paper summarizes the first available proof and results for general full, so space and time discretizations for center manifolds of nonlinear parabolic problems. They have to admit a local time dependent solution (a germ) near the bifurcation point.
openaire +1 more source
Center Manifolds and Bifurcation Theory
2013Let \(F:{\mathbb R}^n\rightarrow {\mathbb R}^n\) be a \(C^1\) vector field with \(F(0)=0\). A center manifold for \(F\) at \(0\) is an invariant manifold containing \(0\) which is tangent to and of the same dimension as the center subspace of \(DF(0)\).
openaire +1 more source