Open AccessParameter estimation of nonlinear map based on second-order discrete variational method
Author(s) -
Xiaoqun Cao
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.080506
Subject(s) - hessian matrix , nonlinear system , mathematics , variational method , chaotic , mathematical analysis , computer science , physics , quantum mechanics , artificial intelligence
In this paper a method is proposed to estimate the unknown parameters of nonlinear map based on the second-order discrete variational method. On the basis of adjoint equations and gradient expressions of cost functional derived from variational method, the second-order adjoint equations and the exact formulas for the Hessian-vector product are educed using the second-order discrete variational method. A new algorithm is given for estimating the unknown parameters of nonlinear maps. The numerical simulations show that all unknown physical parameters of Hyperhenón map and two-dimensional parabolic map are estimated successfully and precisely. Simulation results also demonstrate the validity and advantages of second-order discrete variational method of estimating the parameters of the discrete chaotic systems.