Rafael Alves da Costa

Bio: Rafael Alves da Costa is an academic researcher from University of São Paulo. The author has contributed to research in topics: Chaotic & Signal processing. The author has an hindex of 3, co-authored 8 publications receiving 23 citations. Previous affiliations of Rafael Alves da Costa include Universidade Federal do ABC.

Spectral Properties of Chaotic Signals Generated by the Bernoulli Map

Abstract: In the last decades, the use of chaotic signals as broadband carriers has been considered in Telecommunications. Despite the relevance of the frequency domain analysis in this field, there are few studies that are concerned with spectral properties of chaotic signals. Bearing this in mind, this paper aims the characterization of the power spectral density (PSD) of chaotic orbits generated by Bernoulli maps. We obtain analytic expressions for autocorrelation sequence, PSD and essential bandwidth for chaotic orbits generated by this map as function of the family parameter and Lyapunov exponent. Moreover, we verify that analytical expressions match numerical results. We conclude that the power of the generated orbits is concentrated in low frequencies for all parameters values. Besides, it is possible to obtain chaotic narrowband signals.

New Trends in Chaos-Based Communications and Signal Processing

Abstract: In the last decades many possible applications of nonlinear dynamics in communication systems and signal processing have been reported. Conversely, techniques usually employed by the signal processing and communication systems communities, as correlation, power spectral density analysis, and linear filters, among others have been used to characterize chaotic dynamical systems. This chapter presents four works that aim to use tools from both fields to generate new and interesting results: (1) a message authentication system based on chaotic fingerprint; (2) a study of the spectral characteristics of the chaotic orbits of the Henon map; (3) an investigation of the chaotic nature of the signals generated by a filtered Henon map, and (4) a communication system that presents equalization and a switching scheme between chaos-based and conventional modulations.

Thermodynamics of Chaotic Systems — An introduction

Abstract: Since the classical work of Boltzmann and Poincare, the complex motion in nonlinear dissipative systems has been described in two ways: either by kinetic theory methods (thermodynamics of irreversible nonlinear processes) or on the basis of the dynamical theory of Poincare, developed initially for Hamiltonian systems. Until recently these theories have been developing practically independently. The rapid growth of the statistical theory of open systems and particularly the theory of self-organisation makes it imperative to synthesise now these two scientific directions. This is the aim of Th ermo-dynamics of Chaotic Sys tem s. In this book the thermodynamic concepts serve to provide an analysis of nonlinear dissipative dynamical systems with complex behaviour. The book provides an elementary and readable introduction to the subject which undoubtedly will be useful to a wide spectrum of readers, not only to physicists, but also specialists from other disciplines. No special mathematical knowledge is expected of the reader. The main aim of the book is to stress interesting and deep analogies between thermodynamic methods in non-linear chaotic dynamics and the generally accepted statistical-mechanics concepts. The book consists of five parts. Part I ''Essentials of nonlinear dynamics'' provides a brief elementary account of the main concepts and phenomena from the theory of nonlinear dynamical systems. Part II ''Essentials of information theory and thermo-dynamics'' presents the main concepts used in thermodynamic analysis of chaotic systems. The authors define the Shannon information measure, the information gain (Kullback entropy), and the Renyi information, and they discuss in detail the general properties of these quantities. The results from thermodynamics, essential for the understanding of the later material, are given in this part. In Part III ''Thermodynamics of multifractals'' the thermodynamic method is used to analyse the distribution of probabilities in the case of complex fractal structures. An important concept of 'escort distributions' is introduced: they represent canonical distributions from statistical thermodynamics. They can be used to derive the main thermodynamic relationships for chaotic systems. Part IV ''Dynamical analysis of chaotic systems'' deals with the time evolution of chaotic dynamical systems. Important quantities representing nonlinear systems, such as the Renyi dimensions, the dynamical Renyi entropy, and the generalised Lyapunov (spelt Liapunov in this book) exponents are analysed on the basis of the free-energy density in the 'thermodynamic limit'. This concept is used for mapping in the limiting case when the size of the cells in the phase space tends to zero …

Finite Time Chaos Synchronization in Time-Delay Channel and Its Application to Satellite Image Encryption in OFDM Communication Systems

Abstract: This paper proposes a finite time chaos synchronization approach for the secure communication of satellite imaging. To this end, chaotic oscillators are considered in both the transmitter and receiver ends to generate the chaotic encryption/decryption keys. To mitigate the non-negligible channel time-delay between the receiver and transmitter, we propose a robust controller design. The proposed approach is designed based on the Lyapunov stability theory and the finite-time synchronization concept to attain finite time synchronization in a time-delayed channel. By using synchronized chaotic keys, a physical-layer chaotic encryption scheme for transmitting the satellite images is designed in orthogonal frequency-division multiplexing wireless network. The proposed chaotic-based satellite image encryption/decryption system is validated using a numerical simulation study. Additionally, to analyse the robustness and demonstrate the efficiency of the proposed chaotic encryption structure, a set of security analysis tools such as histogram analysis, key space analysis, correlation test, information entropy and other statistical analysis were performed.

A New Four-Dimensional Non-Hamiltonian Conservative Hyperchaotic System

Abstract: This paper presents a new four-dimensional non-Hamiltonian conservative hyperchaotic system. In the absence of equilibrium points in the system, the phase trajectories generated by the system have ...

On the correlation of chaotic signals generated by multimodal skew tent map

Abstract: In recent years, a great deal of attention has been devoted to the application of chaos theory in signal processing and communications. Despite the importance of spectral analysis in these domains, there are few works that take an interest in spectral properties of chaotic signals. In this work, we derive analytic expressions for the autocorrelation function and the auto-spectral density function of chaotic signals generated by a multimodal skew tent map. Our results reveal that chaotic signals generated from a multimodal skew tent map have similar spectral properties to those generated from a unimodal skew tent map.