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Isochronicity of centers at a center manifold
AIP Conference Proceedings, 2012For a three dimensional system with a center manifold filled with closed trajectories (corresponding to periodic solutions of the system) we give criteria on the coefficients of the system to distinguish between the cases of isochronous and non-isochronous oscillations. Bifurcations of critical periods of the system are studied as well.
Brigita Ferčec, Matej Mencinger
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1976
In this section we will start to carry out the program outlined in Section 1 by proving the center manifold theorem. The general invariant manifold theorem is given in Hirsch-Pugh-Shub [1]. Most of the essential ideas are also in Kelley [1] and a treatment with additional references is contained in Hartman [1]. However, we shall follow a proof given by
J. E. Marsden, M. McCracken
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In this section we will start to carry out the program outlined in Section 1 by proving the center manifold theorem. The general invariant manifold theorem is given in Hirsch-Pugh-Shub [1]. Most of the essential ideas are also in Kelley [1] and a treatment with additional references is contained in Hartman [1]. However, we shall follow a proof given by
J. E. Marsden, M. McCracken
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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
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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
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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 ...
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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 ...
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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.
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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.
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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.
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Cancer risk among World Trade Center rescue and recovery workers: A review
Ca-A Cancer Journal for Clinicians, 2022Paolo Boffetta +2 more
exaly