Carlos Souza

Bio: Carlos Souza is an academic researcher from Federal University of Pernambuco. The author has contributed to research in topics: Chaotic & Symbolic dynamics. The author has an hindex of 3, co-authored 11 publications receiving 29 citations.

A smooth chaotic map with parameterized shape and symmetry

Abstract: We introduce in this paper a new chaotic map with dynamical properties controlled by two free parameters. The map definition is based on the hyperbolic tangent function, so it is called the tanh map. We demonstrate that the Lyapunov exponent of the tanh map is robust, remaining practically unaltered with the variation of its parameters. As the main application, we consider a chaotic communication system based on symbolic dynamics with advantages over current approaches that use piecewise linear maps. In this context, we propose a new measure, namely, the spread rate, to study the local structure of the chaotic dynamics of a one-dimensional chaotic map.

Digital Communication Systems Based on Three-Dimensional Chaotic Attractors

Abstract: In this paper, we propose a methodology to design chaos-based communication systems, which exploits the topological structure of 3-D chaotic attractors. The first step consists in defining a proper partition of a Poincare section of the attractor and the subsequent encoding of the chaotic trajectories. Then, the evolution mechanism of the chaotic attractor, according to the dynamical restrictions imposed by the chaotic flow, is represented by a state diagram, where each state represents a region of the Poincare section or a branch in the template of the chaotic attractor. The state transitions are associated with segments of chaotic trajectories that connect the corresponding regions of the Poincare section. The chaotic signals are transmitted over both additive white Gaussian noise and Rayleigh flat fading channels, and a trellis structure derived from the state diagram is used at the decoder to estimate the transmitted information sequence. Finally, the bit error rate performance of the system is analyzed.

One-Dimensional Pseudo-Chaotic Sequences Based on the Discrete Arnold’s Cat Map Over ℤ₃ ᵐ

Abstract: In this brief we employ the discrete Arnold’s cat map over the integer ring $\mathbb {Z}_{3^{m}}$ to construct one-dimensional pseudo-chaotic sequences. We analyze their period properties using the properties of the Fibonacci sequence over $\mathbb {Z}_{3^{m}}$ and show that they have twice the period of the sequences generated by the logistic map over $\mathbb {Z}_{3^{m}}$ recently proposed. Moreover, we investigate the pseudo-chaotic properties of the proposed sequences in the context of pseudo-chaos. Finally, these sequences are employed to design a pseudo-random number generator and a statistical analysis with the NIST statistical test suite is performed.

A new map for chaotic communication

Abstract: We propose in this paper a new one-dimensional chaotic map based on the hyperbolic tangent function that depends on a single control parameter r. The Lyapunov exponent of this map remains practically unaltered with the variation of r. Two new statistics are proposed to study the chaotic dynamic characteristics of chaotic maps, namely, the spread rate, and the contraction factor. The proposed map may be employed in chaotic communication systems based on symbolic dynamics with advantages over current approaches that uses piecewise linear maps.

A Symbolic Dynamics Approach to Trellis-Coded Chaotic Modulation

Abstract: We propose a trellis-coded chaotic modulation scheme employing the symbolic dynamics generated by three-dimensional chaotic flows. The continuous chaotic trajectories are discretized using a labeled partition of a Poincare section. The discrete dynamics is modeled by a graph representing the evolution mechanism of the chaotic trajectories according to the restrictions imposed by the chaotic flow. This graph is employed to design finite-state encoders to transmit binary information sequences using the restricted discrete chaotic dynamics. We show that the proposed system outperforms a recently proposed trellis-coded chaotic modulation scheme.

Statistics of conductance and shot-noise power for chaotic cavities

Abstract: We report on an analytical study of the statistics of conductance, $g$, and shot-noise power, $p$, for a chaotic cavity with arbitrary numbers $N_{1,2}$ of channels in two leads and symmetry parameter $\beta = 1,2,4$. With the theory of Selberg's integral the first four cumulants of $g$ and first two cumulants of $p$ are calculated explicitly. We give analytical expressions for the conductance and shot-noise distributions and determine their exact asymptotics near the edges up to linear order in distances from the edges. For $0

A Framework for Investigating the Performance of Chaotic-Map Truly Random Number Generators

Abstract: In this paper, we approximate the hidden Markov model of chaotic-map truly random number generators (TRNGs) and describe its fundamental limits based on the approximate entropy-rate of the underlying bit-generation process. We demonstrate that entropy-rate plays a key role in the performance and robustness of chaotic-map TRNGs, which must be taken into account in the circuit design optimization. We further derive optimality conditions for post-processing units that extract truly random bits from a raw-RNG.

Emitter-coupled pair chaotic generator circuit

Abstract: An emitter-coupled pair chaotic generator is proposed with a control parameter that can be tuned for distinct chaotic behaviors. The proposed circuit is a compact, high-speed implementation of the chaotic map based on the hyperbolic tangent function. It is demonstrated that the circuit and map parameters are analytically related. As an application, we design a random number generator that passes all NIST statistical tests by applying a post-processing to the balanced bit sequence generated by a quantization of the circuit output.

Digital Communication Systems Based on Three-Dimensional Chaotic Attractors

Abstract: In this paper, we propose a methodology to design chaos-based communication systems, which exploits the topological structure of 3-D chaotic attractors. The first step consists in defining a proper partition of a Poincare section of the attractor and the subsequent encoding of the chaotic trajectories. Then, the evolution mechanism of the chaotic attractor, according to the dynamical restrictions imposed by the chaotic flow, is represented by a state diagram, where each state represents a region of the Poincare section or a branch in the template of the chaotic attractor. The state transitions are associated with segments of chaotic trajectories that connect the corresponding regions of the Poincare section. The chaotic signals are transmitted over both additive white Gaussian noise and Rayleigh flat fading channels, and a trellis structure derived from the state diagram is used at the decoder to estimate the transmitted information sequence. Finally, the bit error rate performance of the system is analyzed.