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 examine the collective behaviour of coupled Duffing Hamiltonian systems (HS) and show the existence of measure synchronization (MS) in the quasi-periodic (QP) and -chaotic states. We show that the dynamics of coupled Duffing Hamiltonians exhibit a transition to coherent invariant measure, their orbits sharing the same phase space as the coupling strength is increased. Transitions from QP mea...

We present an innovative adaptive, model following control scheme and apply it to control a chaotic system with unknown parameters. We illustrate the proposed approach with control of Duffing oscillator problem. The same idea is used to solve three important problems: suppression of chaos, anticontrol of chaos and chaos synchronization. We propose to use ‘approximators’ linearly parameterized b...

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 present an experimental set-up that allows to study both controlled and uncontrolled synchronization between a variety of different type of oscillators. The setup consists of two fully actuated mass-damper-spring oscillators mounted on an actuated platform. By means of different types of feedback realized through computer controlled actuation it is possible to demonstrate different synchroni...

In this paper, a method for identifying the chaotic state of duffing oscillator is proposed where the duffing oscillator is used for weak signal detection. This method is based on frequency spectrum analysis and filtering. Some relative aspects of this method for practical using are studied in details too. The proposed method has three properties; reasonable calculation complexity, robustness t...

We study the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behavior. We study these transitions in detail for small and large numbers of oscillators. P...

The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force f and its frequency Ω. We first examine the stability of the steady state in linear response, and classify the different types of bifurcation likely to occur in this model. We then explore the complex behaviour associated with these bifurcat...

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...