In this paper, we consider the partially nonlinear errors-in-variables models when the non- parametric component is measured with additive error. The profile nonlinear least squares estimator of unknown parameter and the estimator of nonparametric component are constructed, and their asymptotic properties are derived under general assumptions. Finite sample performances of the proposed statistical inference procedures are illustrated by Monte Carlo simulation studies.
By using an extended Melnikov method on multi-degree-of-freedom Hamiltonian systems with perturbations,the global bifurcations and chaotic dynamics are investigated for a parametrically excited,simply supported rectangular buckled thin plate.The formulas of the rectangular buckled thin plate are derived by using the von Karman type equation.The two cases of the buckling for the rectangular thin plate are considered.With the aid of Galerkin's approach,a two-degree-of-freedom nonautonomous nonlinear system is obtained for the non-autonomous rectangular buckled thin plate.The high-dimensional Melnikov method developed by Yagasaki is directly employed to the non-autonomous ordinary differential equation of motion to analyze the global bifurcations and chaotic dynamics of the rectangular buckled thin plate.Numerical method is used to find the chaotic responses of the non-autonomous rectangular buckled thin plate.The results obtained here indicate that the chaotic motions can occur in the parametrically excited,simply supported rectangular buckled thin plate.
