Theoretical Design and Circuit Implementation of Integer Domain Chaotic Systems

Wang, Qianxue; Yu, Simin; Guyeux, Christophe; Bahi, Jacques M.; Fang, Xiaole

doi:10.1142/s0218127414501284

Cited by 23 publications

(11 citation statements)

References 16 publications

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“…The circuit realization is important for the chaotic system, especially by adopting commercially common electronic components [28][29][30]. In this section, we build an electronic circuit to physically realize the reported system for different cases, based on the improved module-based technique 7 Complexity [31][32][33][34]. The electronic circuit is designed as the jerk form by using the dimensionless state equations, as depicted in Figure 12, which is simple with less circuit elements.…”

Section: Circuit Realization Of a Memristor-based Jerk Systemmentioning

confidence: 99%

Dynamical Behavior of a 3D Jerk System with a Generalized Memristive Device

Feng

et al. 2018

Complexity

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As a new type of electronic components, a memristive device is receiving worldwide attention and can enrich the dynamical behaviors of the oscillating system. In this paper, we propose a 3D jerk system by introducing a generalized memristive device. It is found that the dynamical behaviors of the system are sensitive to the initial conditions even the system parameters are fixed, which results in the coexistence of multiple attractors. And there exists different transition behaviors depending on the selection of the parameters and initial values. Thereby, it is one important type of the candidate system for secure communication since the reconstruction of accurate state space becomes more difficult. Moreover, we build a hardware circuit and the experimental results effectively confirm the theoretical analyses.

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Section: Circuit Realization Of a Memristor-based Jerk Systemmentioning

confidence: 99%

Dynamical Behavior of a 3D Jerk System with a Generalized Memristive Device

Feng

et al. 2018

Complexity

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“…Luo et al presented a homeomorphism and showed that an invertible mapping on a compact metric space was Li-Yorke chaotic [25]. Wang et al provided two chaotic systems satisfying Devaney's definition of chaos in [29,30]. In [38], Zheng et al solved the chaotic dynamical degradation problem in real domain by providing an effective schemes with symbolic dynamics.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

Zhu

et al. 2021

Preprint

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Owning to complex properties of ergodicity, non-periodic ability and sensitivity to initial states, chaotic systems are widely used in cryptography. In this paper, we propose a sinusoidal--polynomial composite chaotic system (SPCCS), and prove that it satisfies Devaney's definition of chaos: the sensitivity to initial conditions, topological transitivity and density of periodic points. The experimental results show that the SPCCS has better unpredictability and more complex chaotic behavior than the classical chaotic maps. Furthermore, we provide a new image encryption algorithm combining pixel segmentation operation, block chaotic matrix confusing operation, and pixel diffusion operation with the SPCCS. Detailed simulation results verify effectiveness of the proposed image encryption algorithm.

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“…This is very different from the existing discrete-time chaotic system in infinite precision real number domain, that all bits will participate in all the update operations by the iterative function. Digital chaotic system constructed with the chaos generation strategy controlled by random sequences is proven to satisfy the Devaney's definition of chaos in [19], [20], [21], [22], [23], [24]. Since this system is directly generated in finite precision digital domain, there is no finite precision effect problem, and the binary sequences can be obtained without transformation and combination.…”

Section: Introductionmentioning

confidence: 99%

“…In [21], chaotic combination of two input entropic streams has solved flaws exhibited in the system designed in [20]. The chaos generation strategy was implemented in [22], through a sample-hold circuit and a decoder circuit so as to convert the uniform noise signal into a random sequence. The second chaos generation strategy named Chaotic Bitwise Dynamical System (CBDS) was proposed in [23].…”

Section: Introductionmentioning

confidence: 99%

Constructing Higher-Dimensional Digital Chaotic Systems via Loop-State Contraction Algorithm

Wang,

Yu,

Guyeux

et al. 2021

Preprint

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In recent years, the generation of rigorously provable chaos in finite precision digital domain has made a lot of progress in theory and practice, this article is a part of it. It aims to improve and expand the theoretical and application framework of higher-dimensional digital chaotic system (HDDCS). In this study, topological mixing for HDDCS is strictly proved theoretically at first. Topological mixing implies Devaney's definition of chaos in compact space, but not vise versa. Therefore, the proof of topological mixing improves and expands the theoretical framework of HDDCS. Then, a general design method for constructing HDDCS via loop-state contraction algorithm is given. The construction of the iterative function uncontrolled by random sequences (hereafter called iterative function) is the starting point of this research. On this basis, this article put forward a general design method to solve the problem of HDDCS construction, and a number of examples illustrate the effectiveness and feasibility of this method. The adjacency matrix corresponding to the designed HDDCS is used to construct the chaotic echo state network (ESN) for the Mackey-Glass time series prediction. The prediction accuracy is improved with the increase of the size of the reservoir and the dimension of HDDCS, indicating that higher-dimensional systems have better prediction performance than lower-dimensional systems.

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Theoretical Design and Circuit Implementation of Integer Domain Chaotic Systems

Cited by 23 publications

References 16 publications

Dynamical Behavior of a 3D Jerk System with a Generalized Memristive Device

Dynamical Behavior of a 3D Jerk System with a Generalized Memristive Device

Dynamic Analysis and Cryptographic Application of a Sinusoidal-polynomial Composite Chaotic System

Constructing Higher-Dimensional Digital Chaotic Systems via Loop-State Contraction Algorithm

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