SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Spectral properties of chaotic signals generated by the skew tent map

Chaotic signals have been considered potentially attractive in many signal processing applications ranging from wideband communication systems to cryptography and watermarking. Besides, some devices as nonlinear adaptive filters and phase-locked loops can present chaotic behavior. In this paper, we derive analytical expressions for the autocorrelation sequence, power spectral density and essential bandwidth of chaotic signals generated by the skew tent map. From these results, we suggest possible applications in communication systems. (C) 2009 Elsevier B.V. All rights reserved.

Quantum nonlinear dynamics of continuously measured systems

Classical dynamics is formulated as a Hamiltonian flow in phase space, while quantum mechanics is formulated as unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and classical nonlinear dynamics. Previous solutions have focused on computing quantities associated with a statistical ensemble such as variance or entropy. However a more diner comparison would compare classical predictions to the quantum predictions for continuous simultaneous measurement of position and momentum of a single system, in this paper we give a theory of such measurement and show that chaotic behavior in classical systems fan be reproduced by continuously measured quantum systems.

Exciting dynamical behavior in a network of two coupled rings of Chen oscillators

We study exotic patterns appearing in a network of coupled Chen oscillators. Namely, we consider a network of two rings coupled through a “buffer” cell, with Z3×Z5 symmetry group. Numerical simulations of the network reveal steady states, rotating waves in one ring and quasiperiodic behavior in the other, and chaotic states in the two rings, to name a few. The different patterns seem to arise through a sequence of Hopf bifurcations, period-doubling, and halving-period bifurcations. The network architecture seems to explain certain observed features, such as equilibria and the rotating waves, whereas the properties of the chaotic oscillator may explain others, such as the quasiperiodic and chaotic states. We use XPPAUT and MATLAB to compute numerically the relevant states.

Dynamics of flow: a nonlinear perspective

The aims of this study are to consider the experience of flow from a nonlinear dynamics perspective. The processes and temporal nature of intrinsic motivation and flow, would suggest that flow experiences fluctuate over time in a dynamical fashion. Thus it can be argued that the potential for chaos is strong. The sample was composed of 20 employees (both full and part time) recruited from a number of different organizations and work backgrounds. The Experience Sampling Method (ESM) was used for data collection. Once obtained the temporal series, they were subjected to various analyses proper to the com- plexity theory (Visual Recurrence Analysis and Surrogate Data Analysis). Results showed that in 80% of the cases, flow presented a chaotic dynamic, in that, flow experiences delineated a complex dynamic whose patterns of change were not easy to predict. Implications of the study, its limitations and future research are discussed.

Differential Evolution approach and parameter estimation of chaotic

Parameter estimation still remains a challenge in many important applications. There is a need to develop methods that utilize achievements in modern computational systems with growing capabilities. Owing to this fact different kinds of Evolutionary Algorithms are becoming an especially perspective field of research. The main aim of this thesis is to explore theoretical aspects of a specific type of Evolutionary Algorithms class, the Differential Evolution (DE) method, and implement this algorithm as codes capable to solve a large range of problems. Matlab, a numerical computing environment provided by MathWorks inc., has been utilized for this purpose. Our implementation empirically demonstrates the benefits of a stochastic optimizers with respect to deterministic optimizers in case of stochastic and chaotic problems. Furthermore, the advanced features of Differential Evolution are discussed as well as taken into account in the Matlab realization. Test "toycase" examples are presented in order to show advantages and disadvantages caused by additional aspects involved in extensions of the basic algorithm. Another aim of this paper is to apply the DE approach to the parameter estimation problem of the system exhibiting chaotic behavior, where the well-known Lorenz system with specific set of parameter values is taken as an example. Finally, the DE approach for estimation of chaotic dynamics is compared to the Ensemble prediction and parameter estimation system (EPPES) approach which was recently proposed as a possible solution for similar problems.

Taming Chaotic Circuits

Control algorithms that exploit chaotic behavior can vastly improve the performance of many practical and useful systems. The program Perfect Moment is built around a collection of such techniques. It autonomously explores a dynamical system's behavior, using rules embodying theorems and definitions from nonlinear dynamics to zero in on interesting and useful parameter ranges and state-space regions. It then constructs a reference trajectory based on that information and causes the system to follow it. This program and its results are illustrated with several examples, among them the phase-locked loop, where sections of chaotic attractors are used to increase the capture range of the circuit.

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Sudden changes in chaotic attractors and transient basins in a model for rattling in gearboxes

We consider a model for rattling in single-stage gearbox systems with some backlash consisting of two wheels with a sinusoidal driving; the equations of motions are analytically integrated between two impacts of the gear teeth. Just after each impact, a mapping is used to obtain the dynamical variables. We have observed a rich dynamical behavior in such system, by varying its control parameters, and we focus on intermittent switching between laminar oscillations and chaotic bursting, as well as crises, which are sudden changes in the chaotic behavior. The corresponding transient basins in phase space are found to be riddled-like, with a highly interwoven fractal structure. (C) 2004 Elsevier Ltd. All rights reserved.

A reducing of a chaotic movement to a periodic orbit, of a micro-electro-mechanical system, by using an optimal linear control design

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Chaos control of a nonlinear oscillator with shape memory alloy using an optimal linear control: Part II: Nonideal energy source

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

CRITICAL EXPONENTS and SCALING PROPERTIES FOR THE CHAOTIC DYNAMICS of A PARTICLE IN A TIME-DEPENDENT POTENTIAL BARRIER

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Some remarks on bifurcation analysis of a nonlinear vibrating system excited by a shape memory alloy material (SMA)

In this paper, the dynamical response of a coupled oscillator is investigated, taking in consideration the nonlinear behavior of a SMA spring coupling the two oscillators. Due to the nonlinear coupling terms, the system exhibits both regular and chaotic motions. The Poincaré sections for different sets of coupling parameters are verified. © 2011 World Scientific Publishing Company.