In this paper we have chosen to work with two different approaches solving the inverse problem of calculus variation. The first approach is based on an integral representation Lagrangian function that uses equation motion while second one relies a generalization well known Noether's theorem and constructs directly from motion. As application provide some useful remarks for modified Emden-type t...

We study two dynamical systems for the motion of three planar charged particles with charges nj ∈ {±1}, j = 1, 2, 3. Both dynamical systems are parametric with a parameter α ∈ [0, 1] and have the same nonlinear terms. As α = 0, 1, the dynamical systems have no chaos. However, one dynamical system may create chaos as α varies from zero to one. This may provide an example to show that the homotop...

Controllability problems for different types of nonlinear dynamical systems with delays in control has been studied by several authors with the help of different fixed point theorems [1-15]. In particular in the paper [7] the notion of measure of noncompactness of a set and Darbo’s fixed point theorem are used for the study of the relative controllability for nonlinear systems with lumped multi...

Amazon.com: Non-Linear Time Series: A Dynamical System Approach Oxford Statistical Science Series, 6 9780198523000: Howell Tong: Books.nonlinear time series model from a nonlinear stochastic dynamical system. Only the approach of Smith 1977 based on piecewise linear.Time series analysis for nonlinear dynamical systems with applications to. Vides a computationally viable alternative to a state-o...

Nonlinear stochastic dynamical systems are widely used to model systems across the sciences and engineering. Such models are natural to formulate and can be analyzed mathematically and numerically. However, difficulties associated with inference from time-series data about unknown parameters in these models have been a constraint on their application. We present a new method that makes maximum ...

In this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the Maclaurin series of the exact solution. Nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. These equations equip a significant mathematical model for dynamical systems. The accuracy o...