Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

Li, Chengqing; Feng, Bingbing; Li, Shujun; Kurths, Jüergen; Chen, Guanrong

doi:10.1109/tcsi.2018.2888688

Cited by 213 publications

(121 citation statements)

References 48 publications

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“…The representative image encryption schemes published in year 2018 are reviewed in [50]. The specific properties of chaotic systems, such as initial state sensitive dependence, unpredictability, make them widely studied and applied in the field of information security [8]- [12]. These properties are similar to the counterparts of cryptography [9], [10], [22].…”

Section: Application In Image Secure Communicationmentioning

confidence: 99%

Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode

Wang

Bao

et al. 2019

IEEE Trans. Circuits Syst. I

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167

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High implementation complexity of multi-scroll circuit is a bottleneck problem in real chaos-based communication. Especially, in multi-scroll Chua's circuit, the simplified implementation of piecewise-linear resistors with multiple segments is difficult due to their intricate irregular breakpoints and slopes. To solve the challenge, this paper presents a systematic scheme for synthesizing a Chua's diode with multi-segment piecewiselinearity, which is achieved by cascading even-numbered passive nonlinear resistors with odd-numbered ones via a negative impedance converter. The traditional voltage mode op-amps are used to implement nonlinear resistors. As no extra DC bias voltage is employed, the scheme can be implemented by much simpler circuits. The voltage-current characteristics of the obtained Chua's diode are analyzed theoretically and verified by numerical simulations. Using the Chua's diode and a secondorder active Sallen-Key high-pass filter, a new inductor-free Chua's circuit is then constructed to generate multi-scroll chaotic attractors. Different number of scrolls can be generated by changing the number of passive nonlinear resistor cells or adjusting two coupling parameters. Besides, the system can be scaled by using different power supplies, satisfying the lowvoltage low-power requirement of integrated circuit design. The circuit simulations and hardware experiments both confirmed the feasibility of the designed system.

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Section: Application In Image Secure Communicationmentioning

confidence: 99%

Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode

Wang

Bao

et al. 2019

IEEE Trans. Circuits Syst. I

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167

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“…Here, we demonstrate that, for at least one simple-butprototypical driven, dissipative dynamical system, namely the generalized Bernoulli Map, the abovementioned hopes are dashed. While it has long been known that individual orbits of this map are chaotic in nature, and that even statistical averages are problematic for the particular case of the system parameter = 2, [7][8][9] our present work demonstrates a more serious problem. Even assuming generic values of , and even assuming idealized statistical averages over infinite evolution time and infinite ensemble size, the results of such averages will be inaccurate by factors of order unity.…”

Section: Doi: 101002/adts201900125mentioning

confidence: 89%

A New Pathology in the Simulation of Chaotic Dynamical Systems on Digital Computers

Boghosian

Coveney

Wang

2019

Advcd Theory and Sims

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Systematic distortions are uncovered in the statistical properties of chaotic dynamical systems when represented and simulated on digital computers using standard IEEE floating-point numbers. This is done by studying a model chaotic dynamical system with a single free parameter , known as the generalized Bernoulli map, many of whose exact properties are known. Much of the structure of the dynamical system is lost in the floating-point representation. For even integer values of the parameter, the long time behaviour is completely wrong, subsuming the known anomalous behaviour for = 2. For non-integer , relative errors in observables can reach 14%. For odd integer values of , floating-point results are more accurate, but still produce relative errors two orders of magnitude larger than those attributable to roundoff. The analysis indicates that the pathology described, which cannot be mitigated by increasing the precision of the floating point numbers, is a representative example of a deeper problem in the computation of expectation values for chaotic systems. The findings sound a warning about the uncritical application of numerical methods in studies of the statistical properties of chaotic dynamical systems, such as are routinely performed throughout computational science, including turbulence and molecular dynamics.Extreme sensitivity to initial conditions is a defining feature of chaotic dynamical systems. Since the first usage of digital computers for computational science, it has been known that loss of precision due to the discrete approximation of

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“…Chaos has inherent randomness and ergodicity [34,35]. It allows the chaotic search to be programmed and traverses every state in a certain search region, while every state is visited only once.…”

Section: Chaotic Searchmentioning

confidence: 99%

Improved Chaotic Quantum-Behaved Particle Swarm Optimization Algorithm for Fuzzy Neural Network and Its Application

Peng

Lei

Yang

et al. 2020

Mathematical Problems in Engineering

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Traditional fuzzy neural network has certain drawbacks such as long computation time, slow convergence rate, and premature convergence. To overcome these disadvantages, an improved quantum-behaved particle swarm optimization algorithm is proposed as the learning algorithm. In this algorithm, a new chaotic search is introduced, and benchmark function experiments prove it outperforms the other five existing algorithms. Finally, the proposed algorithm is presented as the learning algorithm for Takagi-Sugeno fuzzy neural network to form a new neural network, and it is utilized in the water quality evaluation of Dongjiang Lake of Hunan province. Simulation results demonstrated the effectiveness of the new neural network.

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Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

Cited by 213 publications

References 48 publications

Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode

Generating Multi-Scroll Chua’s Attractors via Simplified Piecewise-Linear Chua’s Diode

A New Pathology in the Simulation of Chaotic Dynamical Systems on Digital Computers

Improved Chaotic Quantum-Behaved Particle Swarm Optimization Algorithm for Fuzzy Neural Network and Its Application

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