Generating multicluster conservative chaotic flows from a generalized Sprott-A system

Cang, Shijian; Li, Yue; Kang, Zhijun; Wang, Zenghui

doi:10.1016/j.chaos.2020.109651

Cited by 28 publications

(9 citation statements)

References 41 publications

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“…According to p, the Minkowski distance has three common forms: 1) p=1, d n,j is the Manhattan distance, i.e., the summation of absolute differences; 2) p=2, d n,j is the Euclidean distance; 3) p=∞, d n,j is the Chebyshev distance, the maximum difference among all the distances. Among these measures, the Chebyshev distance, i.e., the maximum norm, is the most common vector distance in probability estimations [17,18,19,20,21] for determining whether all differences of values in two state vectors fall inside a given threshold.…”

Section: Heaviside Kernel Probability Estimationmentioning

confidence: 99%

“…Currently, model-free estimators, particularly those based on kernel functions (e.g., the Heaviside function) in reconstructed state spaces are particularly popular [16]. Kernel estimation for the state space distance has been widely adopted in informational statistics, such as for entropy estimation [17,18,19,20], causality detection [12,21,22], and networked connections [23,24]. Overall, kernel-based estimators have been used to determine the dynamical complexity of time series in subjects ranging from physics to economics and physiology.…”

Section: Introductionmentioning

confidence: 99%

“…To estimate the probability distribution, the elements in the original series are reconstructed into state spaces, and the probability of the series is calculated indirectly using the distribution of the target spaces. For the Heaviside kernel, the probability distribution of the original process becomes that of the maximum norm differences (i.e., the Chebyshev distance) between space vectors that are within a given tolerance [12,17,18,19,20,21]. Vectors with spatial distances no larger than the threshold are assumed to have the same structural information and are employed in the probability estimation, while those with differences greater than the threshold are discarded.…”

Section: Introductionmentioning

confidence: 99%

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A novel parameter for nonequilibrium analysis in reconstructed state spaces

Yao,

Wang

2021

Preprint

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Kernel methods are widely used for probability estimation by measuring the distribution of low-passed vector distances in reconstructed state spaces. However, the information conveyed by the vector distances that are greater than the threshold has received little attention. In this paper, we consider the probabilistic difference of the kernel transformation in reconstructed state spaces, and derive a novel nonequilibrium descriptor by measuring the fluctuations of the vector distance with respect to the tolerance. We verify the effectiveness of the proposed kernel probabilistic difference using three chaotic series (logistic, Henon, and Lorenz) and a firstorder autoregressive series according to the surrogate theory, and we use the kernel parameter to analyze real-world heartbeat data. In the heartbeat analysis, the kernel probabilistic difference, particularly that based on the Kullback-Leibler divergence, effectively characterizes the physiological complexity loss related to reduced cardiac dynamics in the elderly and diseased heartbeat data. Overall, the kernel probabilistic difference provides a novel method for the quantification of nonequilibria by characterizing the fluctuation theorem in reconstructed state spaces, and enables reliable detection of cardiac physiological and pathological information from heart rates.

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Section: Heaviside Kernel Probability Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A novel parameter for nonequilibrium analysis in reconstructed state spaces

Yao,

Wang

2021

Preprint

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“…Although, it can be observed that no control procedure is applied for synchronization of this system. In [45], a new chaotic system with interesting characteristic is derived from Sprott chaotic system, but, the synchronization problem is ignored. Additionally, by analyzing the researches [46][47][48][49] which are related to Sprott's chaotic system, it can be found that no comprehensive work is investigated and proposed the synchronization problem in the existence of parametric uncertainty, time-delay and external disturbance for Sprott's chaotic system.…”

Section: Introductionmentioning

confidence: 99%

A Disturbance-Observer-Based Sliding Mode Control for the Robust Synchronization of Uncertain Delayed Chaotic Systems: Application to Data Security

et al. 2021

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This paper proposes a disturbance observer-based Sliding Mode Control (SMC) approach for the robust synchronization of uncertain delayed chaotic systems. This is done by, first, examining and analyzing the electronic behavior of the master and slave Sprott chaotic systems. Then, synthesizing a robust sliding mode control technique using a newly proposed sliding surface that encompasses the synchronization error between the master and slave. The external disturbances affecting the system were estimated using a disturbance observer. The proof of the semi-globally bounded synchronization between the master and slave was established using the Lyapunov stability theory. The efficiency of the proposed approach was first assessed using a simulation study, then, experimentally validated on a data security system. The obtained results confirmed the robust synchronization properties of the proposed approach in the presence of timedelays and external disturbances. The experimental validation also confirmed its ability to ensure the secure transfer of data. INDEX TERMS Sliding mode control; robust synchronization control; chaotic systems; disturbance observer; data security.

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“…Since the occurrence of chaotic behavior in the system's dynamic has always been taken into consideration, numerous investigations have been performed on particular characteristics of chaotic or nonlinear systems, and diverse systems have been introduced. In other words, some researchers have introduced multistable [6][7][8][9], megastable [10][11][12], extreme multistable [13][14][15], variable-boostable [16,17], memristor-based [18][19][20], conservative [21][22][23], multicluster [24], or any kinds of symmetrical systems [25][26][27][28]. For instance, the paper proposed by Bao et al has introduced a nonautonomous 2D neural system and has also studied the multistability of the defined model [7].…”

Section: Introductionmentioning

confidence: 99%

A New Circumscribed Self‐Excited Spherical Strange Attractor

Ramamoorthy¹,

Jamal

Hussain

et al. 2021

Complexity

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Studying new chaotic flows with specific characteristics has been an open-ended field of exploring nonlinear dynamics. Investigation of chaotic flows is an area of research that has been taken into consideration for many years; thus, it helps in a better understanding of the chaotic systems. In this paper, an original chaotic 3D system, which has not been investigated yet, is presented in spherical coordinates. A unique feature of the proposed system is that its velocity becomes zero for a specific value of the radius variable. Hence, the system’s attractor is expected to be stuck on one side of a plane in spherical coordinates and inside or outside a sphere in the corresponding Cartesian coordinates. It means that the attractor cannot pass through the sphere or even touch it. The introduced system owns two unstable equilibria and a self-excited strange attractor. The 1D and 2D system’s bifurcation diagrams concerning the alteration of two bifurcation parameters are plotted to investigate the system’s dynamical properties. Moreover, the system’s Lyapunov exponents in the corresponding period of bifurcation parameters are calculated. Then, two 2D basins of attraction for two different third dimension values are explored. Based on the basin of attraction, it can be found that the sphere has attraction itself, partially, and some initial conditions are led to the sphere, not to the strange attractor. Ultimately, the connecting curves of the proposed system are explored to find an informative 1D set in addition to the system’s equilibria.

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Generating multicluster conservative chaotic flows from a generalized Sprott-A system

Cited by 28 publications

References 41 publications

A novel parameter for nonequilibrium analysis in reconstructed state spaces

A novel parameter for nonequilibrium analysis in reconstructed state spaces

A Disturbance-Observer-Based Sliding Mode Control for the Robust Synchronization of Uncertain Delayed Chaotic Systems: Application to Data Security

A New Circumscribed Self‐Excited Spherical Strange Attractor

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