We study microwave response of a Josephson parametric oscillator consisting superconducting transmission-line resonator with an embedded DC-superconducting quantum interference device (-SQUID). The DC-SQUID allows to control the magnitude Kerr nonlinearity over ranges where it is smaller or larger than photon loss rate. Spectroscopy measurements reveal change in from classical Duffing single de...

The subject of this paper is the existence, uniqueness and stability solutions for a new sequential Van der Pol–Duffing (VdPD) jerk fractional differential oscillator with Caputo–Hadamard derivatives. arguments are based upon Banach contraction principle, Krasnoselskii fixed-point theorem Ulam–Hyers stabilities. As applications, one illustrative example included to show applicability our results.

The current paper focuses on some analytical techniques to solve the non-linear Duffing oscillator with large nonlinearity. Four different methods have been applied for solution of the equation of motion; the variational iteration method, He’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. The results reveal that approxim...

Ordinal patterns are a time-series data analysis tool used as preliminary step to construct the permutation entropy, which itself allows same characterization of dynamics chaotic or regular more theoretical constructs such Lyapunov exponent. However, ordinal store strictly information than entropy exponents. We present results working with Duffing oscillator showing that reflect changes in dyna...

The stable and unstable manifolds associated with a saddle point in two-dimensional non–areapreserving flows under general time-aperiodic perturbations are examined. An improvement to existing geometric Melnikov theory on the normal displacement of these manifolds is presented. A new theory on the previously neglected tangential displacement is developed. Together, these enable locating the per...

Adaptive oscillators are a type of nonlinear oscillator that capable learning and storing information in plastic states. Here, typical mechanical pendulum is modified to have an adjustable rod length create adaptive frequency oscillator. Since the resonance function length, this allows learn encode from external source. An experimental designed constructed, its performance compared numerical si...