Jos&#233; Roberto Castilho Piqueira

Elbert E. Neher Macau

Celso Grebogi

Modeling Experimental Nonlinear Dynamics and Chaotic Scenarios

This work presents the analysis of nonlinear aeroelastic time series from wing vibrations due to airflow separation during wind tunnel experiments. Surrogate data method is used to justify the application of nonlinear time series analysis to the aeroelastic system, after rejecting the chance for nonstationarity. The singular value decomposition (SVD) approach is used to reconstruct the state space, reducing noise from the aeroelastic time series. Direct analysis of reconstructed trajectories in the state space and the determination of Poincaré sections have been employed to investigate complex dynamics and chaotic
patterns. With the reconstructed state spaces, qualitative analyses may be done, and the attractors evolutions with parametric variation are presented. Overall results reveal complex system dynamics associated with highly separated  flow effects together with nonlinear coupling between aeroelastic modes. Bifurcations to the nonlinear aeroelastic system are observed for two investigations, that is, considering oscillations-induced aeroelastic evolutions with varying freestream speed, and aeroelastic evolutions at constant freestream speed and varying oscillations. Finally, Lyapunov exponent calculation is proceeded in order to infer on chaotic behavior. Poincaré mappings also suggest bifurcations and chaos, reinforced by the attainment of maximum positive Lyapunov exponents.

F. D. Marques

R. M. G. Vasconcellos

Chaotic Patterns in Aeroelastic Signals

In this paper, we have presented a new permutation-substitution image encryption architecture using chaotic maps and Tompkins-Paige algorithm. The proposed encryption system includes two major parts, chaotic pixels permutation and chaotic pixels substitution. A logistic map is used to generate a bit sequence, which is used to generate pseudorandom numbers in Tompkins-Paige algorithm, in 2D permutation phase. Pixel substitution phase includes two process, the tent pseudorandom image (TPRI) generator and modulo addition operation. All parts of the proposed chaotic encryption system are simulated. Uniformity of the histogram of the proposed encrypted image is justified using the chi-square test, which is less than <svg style="vertical-align:-2.53308pt;width:16.924999px;" id="M1" height="16.924999" version="1.1" viewBox="0 0 16.924999 16.924999" width="16.924999" xmlns="http://www.w3.org/2000/svg">
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</svg>(255, 0.05). The vertical, horizontal, and diagonal correlation coefficients, as well as their average and RMS values for the proposed encrypted image are calculated that is about 13&#x25; less than previous researches. To quantify the difference between the encrypted image and the corresponding plain-image, three measures are used. These are MAE, NPCR, and UACI, which are improved in our proposed system considerably. NPCR of our proposed system is exactly the ideal value of this criterion. The key space of our proposed method is large enough to protect the system against any Brute-force and statistical attacks.

Shahram Etemadi Borujeni

Mohammad Eshghi

Chaotic Image Encryption Design Using Tompkins-Paige Algorithm

A combination of trajectory sensitivity method and master-slave synchronization was proposed
to parameter estimation of nonlinear systems. It was shown that master-slave coupling increases the robustness
of the trajectory sensitivity algorithm with respect to the initial guess of parameters. Since synchronization is
not a guarantee that the estimation process converges to the correct parameters, a conditional test that guarantees
 that the new combined methodology estimates the true values of parameters was proposed. This conditional test was
successfully applied to Lorenz&#39;s and Chua&#39;s systems, and the proposed parameter estimation algorithm has shown to be very robust with respect to parameter initial guesses and measurement noise for these examples.

Elmer P. T. Cari

Edson A. R. Theodoro

Ana P. Mijolaro

Newton G. Bretas

Luis F. C. Alberto

Trajectory Sensitivity Method and Master-Slave Synchronization to Estimate Parameters of Nonlinear Systems

The paper presents a linear model of ferroresonant circuit with flux reflection. The proposed model—flux reflection model—derives from observations of typical flux waveforms of nonlinear coil during ferroresonant steady states. Simulation results of the flux reflection model are compared with simulation results of the usual nonlinear model as well as with measurements carried out on the
physical model of the ferroresonant circuit. The flux reflection model enables a novel comprehension
of the ferroresonant circuit behavior and simplifies the modeling of the nonlinear coil in the
ferroresonant circuit.

Kruno Mili&#x010D;evi&#x0107;

Ivan Flegar

Denis Pelin

Flux Reflection Model of the Ferroresonant Circuit

We present a study of the behavior of a ball under the influence of gravity on a platform. A propagating surface wave travels on the surface of the platform while the platform remains motionless. This is a modification of the classical bouncing ball problem and describes the transport of particles by surface waves. Phase and velocity maps cannot be expressed in the explicit form due to implicit formulations, and no formal analytical analyses is possible. Numerical analysis shows that the transition to chaos is produced via a period doubling route which is a common property for classical bouncers. These numerical analysis have been carried out for the conservative and for the viscous cases and also for elastic and for inelastic collisions. The bouncing process can be sensitive to the initial conditions and can be useful for control techniques
which can dramatically increase the effectiveness of particle transport in practical applications. Finally, we
also consider the mechanical model of a particle sliding on a surface which is also important because it has
important physical implications such as the transportation of thin films in biomedical applications, among
others.

Minvydas Ragulskis

Edita Sakyte

Jesús M. Seoane

Miguel A. F. Sanjuán

A New Mechanical Model for Particle Transport by Surface Waves and Applications

An LPV rational order control model of an irrigation canal is derived from system identification
experiments. This model is experimentally obtained by using the described LPV fractional identification procedure. This procedure
consists of the identification of a rational order model in each operation point in an experimental test canal. Global LPV
model is obtained from polynomial interpolation of local model parameters. Validation results demonstrate that rational order
models are more accurate than integer order models. Therefore rational order control models have an important role to play in
management and efficient use of water resources.

Rubén Martínez-González

Yolanda Bolea

Antoni Grau

Herminio Martínez-García

An LPV Fractional Model for Canal Control

As a liquid-liquid system is far from equilibrium state, the phase thickness is variable when mass transfer process with chemical reaction occurs in interphase zone, and a dispersible transitional layer called the interphase dispersed zone (IDZ) is formed. The IZD model composed of thermodynamically instable O/W or W/O microemulsion has reasonably explained enormous experimental phenomena in nonlinear mass transfer. To forecast the possible parameter ranges of IDZ process and abrupt change of liquid-liquid mass transfer rate, the dynamic characteristics of a molecular diffusion model are considered in this paper. We applied the bifurcation theory of planar dynamical system, Laplace transform, and maple software to investigate the model, and obtain different phase portraits of the system in different regions. The results obtained will play an important directive role in the study of IDZ model.

DongXiang Zhang

Min Sun

Jing Li

Analysis of Nonlinear Dynamics for Abrupt Change of Interphase Structure in Liquid-Liquid Mass Transfer

Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.

Marcio Eisencraft

Renato D. Fanganiello

Luiz A. Baccala

Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels

We study the dynamical behavior of a single inductor two inputs two outputs (SITITO)
power electronics DC-DC converter under a current mode control in a PWM interleaved scheme. This
system is able to regulate two, generally one positive and one negative, voltages (outputs). The regulation
of the outputs is carried out by the modulation of two time intervals within a switching cycle. The value
of the regulated voltages is related to both duty cycles (inputs). The stability of the whole nonlinear
system is therefore studied without any decoupling. Under certain operating conditions, the dynamical
behavior of the system can be modeled by a piecewise linear (PWL) map, which is used to investigate the
stability in the parameter space and to detect possible subharmonic oscillations and chaotic behavior.
These results are confirmed by numerical one dimensional and two-dimensional bifurcation diagrams and
some experimental measurements from a laboratory prototype.

Abdelali El Aroudi

Vanessa Moreno-Font

Luis Benadero

Dynamical Analysis of an Interleaved Single Inductor TITO Switching Regulator

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Mathematical Problems in Engineering is a broad-based journal publishing&nbsp;results of rigorous engineering research across all disciplines, carried out using mathematical tools.

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Chief Editor, Professor Guangming Xie, is currently a full professor of dynamics and control with the College of Engineering, Peking University. His research interests include complex system dynamics and control and intelligent and biomimetic robots.

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Mathematical Problems in Engineering

Modeling Experimental Nonlinear Dynamics and Chaotic Scenarios

Modeling Experimental Nonlinear Dynamics and Chaotic Scenarios

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