Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System

He, Shaobo; Sun, Kehui; Wang, Huihai

doi:10.3390/e17127882

Cited by 174 publications

(99 citation statements)

References 32 publications

(36 reference statements)

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“…Moreover, Mou et al [12] designed a memory circuit with two memcapacitors that exhibited complex phenomena of state transition and transient chaos accompanied with time evolution and coexisting states. Fractional calculus has been studied for about 300 years, and there are a large number of literatures reporting chaos in the fractional-order nonlinear systems [17][18][19][20]. Moreover, fractional-order memory electronic element-based systems increasingly attracted attention of scholars [21,22].…”

Section: Introductionmentioning

confidence: 99%

Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

Banerjee

2018

Complexity

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Application of conformable fractional calculus in nonlinear dynamics is a new topic, and it has received increasing interests in recent years. In this paper, numerical solution of a conformable fractional nonlinear system is obtained based on the conformable differential transform method. Dynamics of a conformable fractional memcapacitor (CFM) system is analyzed by means of bifurcation diagram and Lyapunov characteristic exponents (LCEs). Rich dynamics is found, and coexisting attractors and transient state are observed. Symbol complexity of the CFM system is estimated by employing the symbolic entropy (SybEn) algorithm, symbolic spectral entropy (SybSEn) algorithm, and symbolic C 0 (SybC 0 ) algorithm. It shows that pseudorandom sequences generated by the system have high complexity and pass the rigorous NIST test. Results demonstrate that the conformable memcapacitor nonlinear system can also be a good model for real applications.

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Section: Introductionmentioning

confidence: 99%

Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

Banerjee

2018

Complexity

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“…Permutation entropy (PE) [20,21] is suitable for measuring the complexity of series of chaos. The larger the value of PE, the more difficult it is to predict the generated chaotic sequence.…”

Section: Analysis Of Permutation Entropymentioning

confidence: 99%

A Novel Delay Linear Coupling Logistics Map Model for Color Image Encryption

Ding

Yin

et al. 2018

Entropy

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Abstract:With the popularity of the Internet, the transmission of images has become more frequent. It is of great significance to study efficient and secure image encryption algorithms. Based on traditional Logistic maps and consideration of delay, we propose a new one-dimensional (1D) delay and linearly coupled Logistic chaotic map (DLCL) in this paper. Time delay is a common phenomenon in various complex systems in nature, and it will greatly change the dynamic characteristics of the system. The map is analyzed in terms of trajectory, Lyapunov exponent (LE) and Permutation entropy (PE). The results show that this map has wide chaotic range, better ergodicity and larger maximum LE in comparison with some existing chaotic maps. A new method of color image encryption is put forward based on DLCL. In proposed encryption algorithm, after various analysis, it has good encryption performance, and the key used for scrambling is related to the original image. It is illustrated by simulation results that the ciphered images have good pseudo randomness through our method. The proposed encryption algorithm has large key space and can effectively resist differential attack and chosen plaintext attack.

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“…But the calculation speed of this algorithm is very slow, and it consumes too many computer resources [15]. Meanwhile, Adomian decomposition method (ADM) [16] is employed to obtain numerical solution of the fractional-order chaotic system for its high precision and fast speed of convergence [17][18][19]. For instance, the fractionalorder Chen system is investigated by Cafagna D et.al [19] by applying ADM, and the results show that it is a good method for solving the fractional-order chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of the Fractional-Order Lorenz System Based on Adomian Decomposition Method and Its DSP Implementation

Sun

Wang

2024

IEEE/CAA J. Autom. Sinica

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Dynamics and digital circuit implementation of the fractional-order Lorenz system are investigated by employing Adomian decomposition method (ADM). Dynamics of the fractional-order Lorenz system with derivative order and parameter varying is analyzed by means of Lyapunov exponents (LEs), bifurcation diagram, chaos diagram and phase diagram. Results show that the fractional-order Lorenz system has rich dynamical behavior and it is a potential model for application. It is also found that the minimum order is affected by numerical algorithm and time step size. Finally, the fractional-order system is implemented on DSP digital circuit. Phase diagrams generated by the DSP are consistent with that generated by simulation.

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Complexity Analysis and DSP Implementation of the Fractional-Order Lorenz Hyperchaotic System

Cited by 174 publications

References 32 publications

Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

A Novel Delay Linear Coupling Logistics Map Model for Color Image Encryption

Dynamics of the Fractional-Order Lorenz System Based on Adomian Decomposition Method and Its DSP Implementation

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