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- Vector_field_reconstruction abstract "Vector field reconstruction is a method of creating a vector field from experimental or computer generated data, usually with the goal of finding a differential equation model of the system.A differential equation model is one that describes the value of dependent variables as they evolve in time or space by giving equations involving those variables and their derivatives with respect to some independent variables, usually time and/or space. An ordinary differential equation is one in which the system's dependent variables are functions of only one independent variable. Many physical, chemical, biological and electrical systems are well described by ordinary differential equations. Frequently we assume a system is governed by differential equations, but we do not have exact knowledge of the influence of various factors on the state of the system. For instance, we may have an electrical circuit that in theory is described by a system of ordinary differential equations, but due to the tolerance of resistors, variations of the supply voltage or interference from outside influences we do not know the exact parameters of the system. For some systems, especially those that support chaos, a small change in parameter values can cause a large change in the behavior of the system, so an accurate model is extremely important. Therefore, it may be necessary to construct more exact differential equations by building them up based on the actual system performance rather than a theoretical model. Ideally, one would measure all the dynamical variables involved over an extended period of time, using many different initial conditions, then build or fine tune a differential equation model based on these measurements.In some cases we may not even know enough about the processes involved in a system to even formulate a model. In other cases, we may have access to only one dynamical variable for our measurements, i.e., we have a scalar time series. If we only have a scalar time series, we need to use the method of time delay embedding or derivative coordinates to get a large enough set of dynamical variables to describe the system.In a nutshell, once we have a set of measurements of the system state over some period of time, we find the derivatives of these measurements, which gives us a local vector field, then determine a global vector field consistent with this local field. This is usually done by a least squares fit to the derivative data.".
- Vector_field_reconstruction wikiPageID "15507968".
- Vector_field_reconstruction wikiPageLength "8490".
- Vector_field_reconstruction wikiPageOutDegree "35".
- Vector_field_reconstruction wikiPageRevisionID "641382746".
- Vector_field_reconstruction wikiPageWikiLink Category:Mathematical_modeling.
- Vector_field_reconstruction wikiPageWikiLink Category:Numerical_analysis.
- Vector_field_reconstruction wikiPageWikiLink Category:Vector_calculus.
- Vector_field_reconstruction wikiPageWikiLink Chaos_theory.
- Vector_field_reconstruction wikiPageWikiLink Cubic_Hermite_spline.
- Vector_field_reconstruction wikiPageWikiLink Degrees_of_freedom_(physics_and_chemistry).
- Vector_field_reconstruction wikiPageWikiLink Delay_embedding.
- Vector_field_reconstruction wikiPageWikiLink Dependent_and_independent_variables.
- Vector_field_reconstruction wikiPageWikiLink Derivative.
- Vector_field_reconstruction wikiPageWikiLink Derivative_coordinates.
- Vector_field_reconstruction wikiPageWikiLink Differential_equation.
- Vector_field_reconstruction wikiPageWikiLink Gram–Schmidt_process.
- Vector_field_reconstruction wikiPageWikiLink Initial_condition.
- Vector_field_reconstruction wikiPageWikiLink Least_squares.
- Vector_field_reconstruction wikiPageWikiLink Lorenz_system.
- Vector_field_reconstruction wikiPageWikiLink Lyapunov_exponent.
- Vector_field_reconstruction wikiPageWikiLink Mathematical_model.
- Vector_field_reconstruction wikiPageWikiLink Ordinary_differential_equation.
- Vector_field_reconstruction wikiPageWikiLink Orthogonal_polynomials.
- Vector_field_reconstruction wikiPageWikiLink Parameter.
- Vector_field_reconstruction wikiPageWikiLink Phase_space.
- Vector_field_reconstruction wikiPageWikiLink Radial_basis_function.
- Vector_field_reconstruction wikiPageWikiLink Resistor.
- Vector_field_reconstruction wikiPageWikiLink Rössler_attractor.
- Vector_field_reconstruction wikiPageWikiLink Singular_value_decomposition.
- Vector_field_reconstruction wikiPageWikiLink Takens_theorem.
- Vector_field_reconstruction wikiPageWikiLink Thermal_lens_oscillations.
- Vector_field_reconstruction wikiPageWikiLink Time_series.
- Vector_field_reconstruction wikiPageWikiLink Vector_field.
- Vector_field_reconstruction wikiPageWikiLink Voltage.
- Vector_field_reconstruction wikiPageWikiLinkText "Vector field reconstruction".
- Vector_field_reconstruction wikiPageUsesTemplate Template:Cleanup.
- Vector_field_reconstruction wikiPageUsesTemplate Template:Essay.
- Vector_field_reconstruction wikiPageUsesTemplate Template:Multiple_issues.
- Vector_field_reconstruction wikiPageUsesTemplate Template:Original_research.
- Vector_field_reconstruction wikiPageUsesTemplate Template:Reflist.
- Vector_field_reconstruction subject Category:Mathematical_modeling.
- Vector_field_reconstruction subject Category:Numerical_analysis.
- Vector_field_reconstruction subject Category:Vector_calculus.
- Vector_field_reconstruction hypernym Method.
- Vector_field_reconstruction type Software.
- Vector_field_reconstruction type Algorithm.
- Vector_field_reconstruction type Page.
- Vector_field_reconstruction type Redirect.
- Vector_field_reconstruction comment "Vector field reconstruction is a method of creating a vector field from experimental or computer generated data, usually with the goal of finding a differential equation model of the system.A differential equation model is one that describes the value of dependent variables as they evolve in time or space by giving equations involving those variables and their derivatives with respect to some independent variables, usually time and/or space.".
- Vector_field_reconstruction label "Vector field reconstruction".
- Vector_field_reconstruction sameAs Q7917823.
- Vector_field_reconstruction sameAs m.03mcqfl.
- Vector_field_reconstruction sameAs Q7917823.
- Vector_field_reconstruction wasDerivedFrom Vector_field_reconstruction?oldid=641382746.
- Vector_field_reconstruction isPrimaryTopicOf Vector_field_reconstruction.