A smooth chaotic map with parameterized shape and symmetry

Chaves, Daniel P. B.; Souza, Carlos; Pimentel, Cecílio

doi:10.1186/s13634-016-0405-4

Cited by 14 publications

(6 citation statements)

References 43 publications

(64 reference statements)

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“…For this family, simple rules can be followed for appropriately tuning the control parameters in order to affect the statistical mean of the resulting time series. Piecewise maps are chosen here, as they are very prominent in applications [3][4][5][18][19][20][21][22][23], and their shape is easy to control. They can also yield chaotic behavior for a wide range of parameter values.…”

Section: Design Of New Chaotic Mapsmentioning

confidence: 99%

Chaotic Maps with Tunable Mean Value—Application to a UAV Surveillance Mission

Moysis,

Lawnik,

Volos

et al. 2023

Symmetry

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Chaos-related applications are abundant in the literature, and span the fields of secure communications, encryption, optimization, and surveillance. Such applications take advantage of the unpredictability of chaotic systems as an alternative to using true random processes. The chaotic systems used, though, must showcase the statistical characteristics suitable for each application. This may often be hard to achieve, as the design of maps with tunable statistical properties is not a trivial task. Motivated by this, the present study explores the task of constructing maps, where the statistical measures like the mean value can be appropriately controlled by tuning the map’s parameters. For this, a family of piecewise maps is considered, with three control parameters that affect the endpoint interpolations. Numerous examples are given, and the maps are studied through a collection of numerical simulations. The maps can indeed achieve a range of values for their statistical mean. Such maps may find extensive use in relevant chaos-based applications. To showcase this, the problem of chaotic path surveillance is considered as a potential application of the designed maps. Here, an autonomous agent follows a predefined trajectory but maneuvers around it in order to imbue unpredictability to potential hostile observers. The trajectory inherits the randomness of the chaotic map used as a seed, which results in chaotic motion patterns. Simulations are performed for the designed strategy.

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Section: Design Of New Chaotic Mapsmentioning

confidence: 99%

Chaotic Maps with Tunable Mean Value—Application to a UAV Surveillance Mission

Moysis,

Lawnik,

Volos

et al. 2023

Symmetry

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“…We apply the union bounds (13) and (17) to evaluate the BER of the proposed communication system. The SNR is defined as SNR =Ē s /N 0 (18) whereĒ s is the average energy of the typical transition curves.…”

Section: A Union Boundmentioning

confidence: 99%

“…Several methods have been proposed to transmit digital information using chaotic waveforms, including chaos control [10], synchronization of chaotic oscillators [11], broadband coherent communication [12], symbolic dynamics with reverse iteration [13]. Multiple access schemes have been proposed using chaos shift keying (CSK), differential chaos shift keying (DSCK) [14], correlation delay shift keying (CDSK) [15].…”

Section: Introductionmentioning

confidence: 99%

Digital Communication Systems Based on Three-Dimensional Chaotic Attractors

2019

Self Cite

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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 Poincaré 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 Poincaré 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 Poincaré 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. INDEX TERMS Chaotic attractors, chaos-based communications, chaos control, error probability, Poincaré section, symbolic dynamics, topology of chaotic systems.

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“…Como uma suposição não restritiva, a análise a seguir considera mapas de pré-imagem binária constante, ou seja, com |S i (y)| = 2 i , i ≥ 0, para todo y pertencenteà imagem de f (•), a não ser por um conjunto finito de pontos. Vários mapas de interesse satisfazem essa propriedade, e.g., mapa da tenda [14], mapa tanh [18], mapa logístico [14], entre outros. A partir de (9), o nível de segurança incondicional depende da incerteza sobre a condição inicial x[0] a partir do conhecimento de x[σ].…”

Section: Seguranç a Incondicionalunclassified

Sistema de Autenticação de Usuário em Camada Física Empregando Sequencias Caóticas

Evangelista¹,

Chaves²,

Pimentel³

2017

Anais De XXXV Simpósio Brasileiro De Telecomunicações E Processamento De Sinais

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Resumo-Em um sistema de comunicação típico, os mecanismos de autenticação são dominantemente implementados em níveis acima da camada física; apesar de haver estratégias (e.g., espalhamento espectral) que são implementadas ao custo de recursos do sistema de comunicação, como maior consumo de banda. Alternativamente, a autenticação pode ser realizada na camada física sem impactar nos requisitos do sistema original e apresentando propriedades adicionais, como: transparente para usuários que não possuem a chave secreta, robustez contra interferência e verificação de identidade de usuário confiável. Este trabalho aborda o projeto e os limitantes deste sistema com o emprego de sequências caóticos. Palavras-Chave-Autenticação de usuário, sequência caótica, segurança incondicional, camada física.

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A smooth chaotic map with parameterized shape and symmetry

Cited by 14 publications

References 43 publications

Chaotic Maps with Tunable Mean Value—Application to a UAV Surveillance Mission

Chaotic Maps with Tunable Mean Value—Application to a UAV Surveillance Mission

Digital Communication Systems Based on Three-Dimensional Chaotic Attractors

Sistema de Autenticação de Usuário em Camada Física Empregando Sequencias Caóticas

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