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...

We develop an approach to reduce the governing equation of motion for the nonlinear vibration of a clamped laminated composite to the Duffing equation in a decoupled modal form. The method of weighted residuals enables such a reduction for laminates with clamped boundary conditions. Both rigidly clamped and loosely clamped boundary conditions are analyzed using this method. The reduction method...

We explore the dynamics of a periodically driven Duffing resonator coupled elastically to a van der Pol oscillator in the case of 1 : 1 internal resonance in the cases of weak and strong coupling. Whilst strong coupling leads to dominating synchronization, the weak coupling case leads to a multitude of complex behaviours. A two-time scales method is used to obtain the frequencyamplitude modulat...

Title of dissertation: NOISE-INFLUENCED DYNAMICS OF NONLINEAR OSCILLATORS J. Edmon Perkins, Doctor of Philosophy, 2015 Dissertation directed by: Professor Balakumar Balachandran Department of Mechanical Engineering Noise is usually considered detrimental to the performance of a system and the effects of noise are usually mitigated through design and/or control. In this dissertation, noise-influ...

The development of closed-loop circuit realizations chaotic synchronization and control is considered a promising aspect analog electronics. Therefore, this paper explores the use sigr function in implementation finite-time terminal sliding mode control. A CFOA-based proposed, whereby an Extended Exploration Grey Wolf Optimization method used to approximate non-integer powered transfer inside f...

A very simple method for synthesizing the inverse system of a non-linear non-autonomous circuit containing nullors is proposed. The main application of the procedure is the synchronization of chaos by the inverse system approach. This is illustrated with two examples: the synchronization of a Duffing circuit and a communication scheme by direct chaotic modulation using Chua’s circuit. ( 1998 Jo...

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...