Vector Field Reconstruction - Applications

Applications

Vector field reconstruction has several applications, and many different approaches. Some mathematicians have not only used radial basis functions and polynomials to reconstruct a vector field, but they have used Lyapunov exponents and singular value decomposition. Gouesbet and Letellier used a multivariate polynomial approximation and least squares to reconstruct their vector field. This method was applied to the Rössler system, and the Lorenz system, as well as thermal lens oscillations.

The Rossler system, Lorenz system and Thermal lens oscillation follows the differential equations in standard system as

X'=Y, Y'=Z and Z'=F(X,Y,Z)

where F(X,Y,Z) is known as the standard function.