Coarse variables of autonomous ODE systems and their evolution
نویسندگان
چکیده
Article history: Received 12 June 2012 Accepted 18 September 2012 Available online 12 October 2012
منابع مشابه
Temporal Coarse-Graining of High-frequency Dynamics Using Parameterized Locally Invariant Manifolds and Practical Time Averaging
Given an autonomous system of ordinary differential equations (ODE), we considerdeveloping practical models for the deterministic, slow/coarse behavior of the ODEsystem. Two types of coarse variables are considered.The first type consists of running finite-time averages of phase functions. We exploretwo strategies to construct the coarse dynamics for such variables. In one, ...
متن کاملModel reduction via parametrized locally invariant manifolds: Some examples
A method for model reduction in non-linear ODE systems is demonstrated through computational examples. The method does not require an implicit separation of time-scales in the fine dynamics to be effective. From the computational standpoint, the method has the potential of serving as a subgrid modeling tool. From the physical standpoint, it provides a model for interpreting and describing histo...
متن کاملOn the choice of coarse variables for dynamics
Two ideas for the choice of an adequate set of coarse variables allowing approximate autonomous dynamics for practical applications are presented. The coarse variables are meant to represent averaged behavior of a fine-scale autonomous dynamics.
متن کاملModeling and Intelligent Control System Design for Overtaking Maneuver in Autonomous Vehicles
The purpose of this study is to design an intelligent control system to guide the overtaking maneuver with a higher performance than the existing systems. Unlike the existing models which consider constant values for some of the effective variables of this behavior, in this paper, a neural network model is designed based on the real overtaking data using instantaneous values for variables. A fu...
متن کاملSOME BOUNDARY VALUE PROBLEMS FOR A NON-LINEAR THIRD ORDER O.D.E.
Existence of periodic solutions for non-linear third order autonomous differential equation (O.D.E.) has not been investigated to as large an extent as non-linear second order. The popular Poincare-Bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). This conclusion opens a way for further investigation.
متن کامل