In this work, we will give an overview of our recent progress in experimental continuation. First, three different approaches are explained and compared which can be found scientific papers on the topic. We then show S-Curve measurements a Duffing oscillator experiment for derived optimal controller gains analytically. The formula stabilizing PD-controller makes trial error search suitable valu...

We study the existence of real-analytic first integrals and integrability for perturbations integrable systems in sense Bogoyavlenskij, including non-Hamiltonian ones. In particular, we assume that there exists a family periodic orbits on regular level set having connected compact component give sufficient conditions nonexistence same number perturbed as unperturbed ones their nonintegrability ...

In a mechanical system x is the displacement and / is the time. We call g(x) a restoring force and ƒ(/) a forcing term. Throughout this paper f{t) will be periodic and when we speak of a periodic solution of (1) we always mean a solution having the same period as ƒ(/). If g(x) is simply a constant multiplied by x, equation (1) represents a linear oscillator. In this case the amplitude of the fo...

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the expansion coefficients. Here we study the structure and dynamics of these differential equations when the original system has Hamiltonian structure, has multiple t...

Many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on Duffing equation. Analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. In this paper, the general form of Duffing equation with cubic nonlinearity as well as par...

We propose a mean-field approach to the Duffing oscillator to construct perturbatively the bounded operators that generate the quantum states, and to define a non-Gaussian density operator. 1 The Duffing oscillator is a typical anharmonic oscillator whose classical aspect is relatively well-understood [1]. It has been studied in many fields of physics from classical mechanics to quantum mechani...

We study persistence of periodic and homoclinic orbits, first integrals commutative vector fields in dynamical systems depending on a small parameter $\varepsilon>0$ give several necessary conditions for their persistence. Here we treat orbits not only to equilibria but also orbits. discuss some relationships these results with the standard subharmonic Melnikov methods time-periodic perturbatio...

It was known to us from decades it is been a factual challenge for us to transfer the privileged data specially images to transfer over a unsecured channel. In this paper we propose a novel image encryption technique using DNA interwearing based Hybridization along with chaotic maps to transfer image data over a unsecured channel. In the early stages we apply Duffing map(chaotic map) on the ori...

In this paper, we prove that the modified PainlevéInce (PI) equation, the force-free Duffing nonlinear type oscillator (DO) and the Lotka-Volterra (LV) nonlinear ordinary differential equation ODEs can be solved in general parametric form. The developed mathematical methodology and the extracted results, being expressed by way of new theorems including admissible functional transformations and ...

Propagation of extremely short pulses of electromagnetic field (electromagnetic spikes) is considered in the framework of the total Maxwell-Duffing model where anharmonic oscillators with cubic nonlinearities (Duffing model) represent the material medium and wave propagation is governed by the 1-d bidirectional Maxwell equations. This system of equations has a one parameter family of exact anal...