Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields
نویسندگان
چکیده
منابع مشابه
Gap bifurcations in nonlinear dynamical systems.
We investigate the dynamics generated by a type of equation which is common to a variety of physical systems where the undesirable effects of a number of self-consistent nonlinear forces are balanced by an externally imposed controlling harmonic force. We show that the equation presents a new sequence of bifurcations where periodic orbits are created and destroyed in such a nonsimultaneous way ...
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We study the structure of the solution set of a class of infinite-horizon dynamic programming problems with one-dimensional state spaces, as well as their bifurcations as problem parameters are varied. The solutions are represented as the integral curves of a multi-valued ‘optimal’ vector field on state space. Generically, there are three types of integral curves: stable points, open intervals ...
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An overview of homoclinic and heteroclinic bifurcation theory for autonomous vector fields is given. Specifically, homoclinic and heteroclinic bifurcations of codimension one and two in generic, equivariant, reversible, and conservative systems are reviewed, and results pertaining to the existence of multi-round homoclinic and periodic orbits and of complicated dynamics such as suspended horses...
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in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولNeural learning of vector fields for encoding stable dynamical systems
The data-driven approximation of vector fields that encode dynamical systems is a persistently hard task in machine learning. If data is sparse and given in form of velocities derived from few trajectories only, state-space regions exists, where no information on the vector field and its induced dynamics is available. Generalization towards such regions is meaningful only if strong biases are i...
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ژورنال
عنوان ژورنال: Journal of Applied Mechanics
سال: 1984
ISSN: 0021-8936,1528-9036
DOI: 10.1115/1.3167759