Case-chaos methodology is a proposed alternative to case-control studies that simulates controls by randomly reshuffling the exposures of cases. We evaluated the method using data on outbreaks in Sweden. We identified 5 case-control studies from foodborne illness outbreaks that occurred between 2005 and 2012. Using case-chaos methodology, we calculated odds ratios 1,000 times for each exposure....

This paper deals with a feedback control strategy for chaos suppression. The proposed strategy is an input–output control scheme which comprises an uncertainty estimator and an asymptotic linearizing feedback. The developed control scheme allows chaos suppression in spite of modeling errors and parametric variations.

This paper proposes an energy efficient control strategy for an induction machine (IM) based on two advanced particle swarm optimisation (PSO) algorithms. Two advanced PSO algorithms, known as the dynamic particle swarm optimisation (Dynamic PSO) and the chaos particle swarm optimisation (Chaos PSO) algorithms modify the algorithm parameters to improve the performance of the standard PSO algori...

Controlling chaos is a topic in nonlinear dynamics which attracted a great deal of work in the last twenty years. Even though there are more definitions of the chaos [4], a distinctive characteristic of the chaotic behavior of a dynamical system is its sensitive dependence on the initial conditions. Generally, chaos is believed to be harmful because in many cases it can lead to disasters. Chaot...

This chapter presents an application of neural networks to chaos synchronization. The two main methodologies, on which the approach is based, are recurrent neural networks and inverse optimal control for nonlinear systems. On the basis of the last technique, chaos is first produced by a stable recurrent neural network; an adaptive recurrent neural controller is then developed for chaos synchron...

This paper illustrates the presence of chaos in rank-one chaotic systems with delay via a binary test called 0-1 test for chaos. Chaotic synchronization between two rank-one chaotic systems without and with delay is achieved by means of Lyapunov functional and linear delayed feedback control method. Numerical simulations are implemented to verify the effectiveness of the proposed chaos synchron...

In this article a symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented. We start by presenting the main properties of chaos and describing some commands with which to obtain qualitative and quantitative measures of chaos, such as the bifurcation diagram and the Lyapunov exponents, respectively. Then we analyze the problem of ch...

This paper deals with the control of chaos exhibited by an impacting mechanical oscillator of one-degree-of-freedom. Its mathematical model is represented by an impulsive hybrid non-autonomous linear dynamics. This dynamics can display attractive nonlinear phenomena such as bifurcations and chaos. In this paper, we propose an approach to control chaos. The proposed strategy is based primarily o...

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this techn...

– We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrödinger and Complex Ginzburg-Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and...