Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map

Wang, Lingyu; Sun, Kehui; Peng, Yuexi; He, Shaobo

doi:10.1016/j.chaos.2019.109488

Cited by 40 publications

(20 citation statements)

References 39 publications

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“…On the other hand, incorporation of fractional calculus with chaotic maps have enriched the dynamical behaviour of maps by demonstrating different distributions in comparison with integer-order counterparts [47]- [52]. According to the investigation results reported in the literature, the main superiorities of fractional-order chaotic maps compared with the integer-order chaotic maps can be summarized as (i) wider chaotic regions can be achieved due to the addition of fractional-order [50], (ii) more random chaotic sequences, more stability, and higher level of security are guaranteed [50], [51], and (iii) better ergodicity and distribution characteristic are illustrated [52]. In this context, researchers have deployed fractional chaotic maps to enhance the performance of optimization algorithms, such as fractional chaotic ensemble particle swarm optimizer [50] and fractional flower pollination algorithm [53].…”

Section: Introductionmentioning

confidence: 91%

Enhanced Fractional Chaotic Whale Optimization Algorithm for Parameter Identification of Isolated Wind-Diesel Power Systems

2020

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Parameters identification of isolated wind-diesel power systems (WDPS) is a significant issue in stability analysis of the power system as well as guaranteeing the power generation through the control system. In this paper, enhanced whale optimization algorithms (EWOA) are proposed to deal with the parameter identification problem of a WDPS system. The proposed EWOA effectively tackles the premature convergence problem of WOA by splitting the population into two subpopulations and updating the position of each whale according to the position of the best agent in its current subpopulation, the position of the other subpopulation's best agent, and the position of the best neighboring agent. Furthermore, fractional chaotic maps are embedded in the search process of EWOA to increase its performance in terms of accuracy. For validation purposes, the proposed algorithms are applied to identify the unknown parameters of WDPS, where different statistical analyzes and comparisons are carried out with other recent state-of-the-art algorithms. Simulation results confirm that the algorithms have less deviation in parameter estimation, more convergence speed, and higher precision in comparison with other algorithms. INDEX TERMS Optimization, parameter identification, whale optimization algorithm, wind-diesel power system.

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Section: Introductionmentioning

confidence: 91%

Enhanced Fractional Chaotic Whale Optimization Algorithm for Parameter Identification of Isolated Wind-Diesel Power Systems

2020

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“…Among them, Caputo definition is more utilized in practical application research due to its more clear physical significance and easy implementation in engineering [31]. So the Caputo definition is used in this paper.…”

Section: The Definitions Of the Fractional Derivativesmentioning

confidence: 99%

“…Entropy measure algorithm is an effective way to analyze the complexity of chaotic system. So far, many entropy measure algorithms such as Shannon entropy [24], fuzzy entropy [25,26], spectral entropy [27][28][29], permutation entropy [30,31], approximate entropy [32][33][34][35] and multiscale permutation entropy [36], have been applied to measure the complexity of chaotic system. Compared with multiscale entropy, multivariate multiscale entropy can observe the dynamic complexity of data in multiple channels [37].…”

Section: Introductionmentioning

confidence: 99%

Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

Zhang

Yang

2021

IEEE Access

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“…As shown in Table 1 , some previous chaos-based ciphers are vulnerable upon various attack methods, including chosen-ciphertext attack [ 16 ], chosen-/known-plaintext attack [ 12 ], differential cryptanalysis [ 17 ], even cipher-only attack [ 18 ]. Therefore, research on security is extremely important and has received much attention [ 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 ].…”

Section: Introductionmentioning

confidence: 99%

Security Analysis of a Color Image Encryption Algorithm Using a Fractional-Order Chaos

Wen

Zhang

Huang

et al. 2021

Entropy

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Fractional-order chaos has complex dynamic behavior characteristics, so its application in secure communication has attracted much attention. Compared with the design of fractional-order chaos-based cipher, there are fewer researches on security analysis. This paper conducts a comprehensive security analysis of a color image encryption algorithm using a fractional-order hyperchaotic system (CIEA-FOHS). Experimental simulation based on excellent numerical statistical results supported that CIEA-FOHS is cryptographically secure. Yet, from the perspective of cryptanalysis, this paper found that CIEA-FOHS can be broken by a chosen-plaintext attack method owing to its some inherent security defects. Firstly, the diffusion part can be eliminated by choosing some special images with all the same pixel values. Secondly, the permutation-only part can be deciphered by some chosen plain images and the corresponding cipher images. Finally, using the equivalent diffusion and permutation keys obtained in the previous two steps, the original plain image can be recovered from a target cipher image. Theoretical analysis and experimental simulations show that the attack method is both effective and efficient. To enhance the security, some suggestions for improvement are given. The reported results would help the designers of chaotic cryptography pay more attention to the gap of complex chaotic system and secure cryptosystem.

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Chaos and complexity in a fractional-order higher-dimensional multicavity chaotic map

Cited by 40 publications

References 39 publications

Enhanced Fractional Chaotic Whale Optimization Algorithm for Parameter Identification of Isolated Wind-Diesel Power Systems

Enhanced Fractional Chaotic Whale Optimization Algorithm for Parameter Identification of Isolated Wind-Diesel Power Systems

Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

Security Analysis of a Color Image Encryption Algorithm Using a Fractional-Order Chaos

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