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...

Nonautonomous forces appear in many applications. They could be periodic, quasiperiodic and almost periodic in time; or they could take the form of a sample path of a random forcing driven by a stochastic process, which is without any periodicity in time. In this paper, we study the chaotic behaviour of differential equations driven by a general nonautonomous forcing without assuming any period...

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...

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states an...

A design scheme of Duffing Chaotic circuit module is proposed based on Multisimin study. The operational amplifier used to construct integrating circuit. chaotic also designed the results can be shown in a virtual oscilloscope by phase trajectory. bifurcation oscillator solved are consistent with that obtained Matlab. equation critical state selected as Chaos Inspection System (CIS), which iden...

The entropy production rate for an open quantum system with a classically chaotic limit has been previously argued to be independent of h and D, the parameter denoting coupling to the environment, and to be equal to the sum of generalized Lyapunov exponents, with these results applying in the near-classical regime. We present results for a specific system going well beyond earlier work, conside...

We have applied the Melnikov criterion to examine a global homoclinic bifurcation and transition to chaos in a case of the Duffing system with nonlinear fractional damping and external excitation. Using perturbation methods we have found a critical forcing amplitude above which the system may behave chaotically. The results have been verified by numerical simulations using standard nonlinear to...

This paper presents a robust indirect model reference fuzzy control scheme for control and synchronization of chaotic nonlinear systems subject to uncertainties and external disturbances. The chaotic system with disturbance is modeled as a Takagi–Sugeno fuzzy system. Using a Lyapunov function, stable adaptation laws for the estimation of the parameters of the Takagi–Sugeno fuzzy model are deriv...