A hidden chaotic attractor in the classical Lorenz system

Munmuangsaen, Buncha; Srisuchinwong, Banlue

doi:10.1016/j.chaos.2017.12.017

Cited by 71 publications

(39 citation statements)

References 31 publications

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“…Common continuous time chaotic systems like Lorenz system [29], Chua's circuit system [30], Jerk system [31], chaotic oscillator [32][33][34], and many hyperchaotic systems have been proposed [35][36][37]. roughout the years, continuous time chaotic systems have been mostly focused on neural network, synchronization, secure communication [38][39][40][41][42], and other elds, especially the design of TRNGs.…”

Section: Trngs Based On Continuous Time Chaoticmentioning

confidence: 99%

A Survey on True Random Number Generators Based on Chaos

Tang

et al. 2019

Discrete Dynamics in Nature and Society

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With the rapid development of communication technology and the popularization of network, information security has been highly valued by all walks of life. Random numbers are used in many cryptographic protocols, key management, identity authentication, image encryption, and so on. True random numbers (TRNs) have better randomness and unpredictability in encryption and key than pseudorandom numbers (PRNs). Chaos has good features of sensitive dependence on initial conditions, randomness, periodicity, and reproduction. These demands coincide with the rise of TRNs generating approaches in chaos field. This survey paper intends to provide a systematic review of true random number generators (TRNGs) based on chaos. Firstly, the two kinds of popular chaotic systems for generating TRNs based on chaos, including continuous time chaotic system and discrete time chaotic system are introduced. The main approaches and challenges are exposed to help researchers decide which are the ones that best suit their needs and goals. Then, existing methods are reviewed, highlighting their contributions and their significance in the field. We also devote a part of the paper to review TRNGs based on current-mode chaos for this problem. Finally, quantitative results are given for the described methods in which they were evaluated, following up with a discussion of the results. At last, we point out a set of promising future works and draw our own conclusions about the state of the art of TRNGs based on chaos.

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Section: Trngs Based On Continuous Time Chaoticmentioning

confidence: 99%

A Survey on True Random Number Generators Based on Chaos

Tang

et al. 2019

Discrete Dynamics in Nature and Society

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“…Thus, it is of great value in theoretical and physical significance and engineering application to study the realization method of hidden attractors. The Chua system, Lorenz-like systems, and the chaotic systems with stable equilibria [10][11][12][13][14][15], line equilibria [16][17][18], or no equilibria [19][20][21][22][23][24] give us impressive points. Hyperchaos with higher complexity is beneficial to secure communication, so some research extends to hyperchaos.…”

Section: Introductionmentioning

confidence: 99%

A Symmetric Controllable Hyperchaotic Hidden Attractor

Zhang

Lei

et al. 2020

Symmetry

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“…A self-excited attractor has its basin of attraction that intersects with the neighborhood of an equilibrium, whereas a hidden attractor has its basin of attraction that does not [20]. Hidden attractors account for the difficulty of finding them since there is no way to choose initial conditions except by an analytical-numerical algorithm [18]- [20], or by an extensive numerical search [21], [22].…”

Section: Introductionmentioning

confidence: 99%

Simple Chaotic Jerk Flows With Families of Self-Excited and Hidden Attractors: Free Control of Amplitude, Frequency, and Polarity

Ahmad

Srisuchinwong

2020

IEEE Access

Self Cite

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Although chaotic systems with self-excited and hidden attractors have been discovered recently, there are few investigations about relationships among them. In this paper, using a systematic exhaustive computer search, three elementary three-dimensional (3D) dissipative chaotic jerk flows are proposed with the unique feature of exhibiting different families of self-excited and hidden attractors. These systems have a variable equilibrium for different values of the single control parameter. In the family of selfexcited attractors, these systems can have a single all-zero-eigenvalue non-hyperbolic equilibrium or two symmetrical hyperbolic equilibria. Besides, for a particular value of the parameter, these systems have no equilibria, and therefore all the attractors are readily hidden. The proposed systems represent a rare class of chaotic systems in which a single system exhibits three different types of equilibria for different values of the single control parameter. In particular, for a single all-zero-eigenvalue non-hyperbolic equilibrium, the coefficient of the two linear terms provides a simple means to rescale the amplitude and frequency, while the introduction of a new constant in the variable x provides a polarity control. Therefore, a free-controlled chaotic signal can be obtained with the desired amplitude, frequency, and polarity. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers and an adjustable DC voltage source, which is convenient for constructing a chaos-based application system.

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A hidden chaotic attractor in the classical Lorenz system

Cited by 71 publications

References 31 publications

A Survey on True Random Number Generators Based on Chaos

A Survey on True Random Number Generators Based on Chaos

A Symmetric Controllable Hyperchaotic Hidden Attractor

Simple Chaotic Jerk Flows With Families of Self-Excited and Hidden Attractors: Free Control of Amplitude, Frequency, and Polarity

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