A simple electronic circuit realization of the tent map

Campos-Cantón, I.; Campos-Cantón, E.; Murguı́a, J. S.; Rosu, H. C.

doi:10.1016/j.chaos.2008.10.037

Cited by 28 publications

(25 citation statements)

References 10 publications

(6 reference statements)

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“…In both Fig. 6(a) and (b), the results about the tent map time series X n that is not employed with the normalization by a factor about ten like in [22] is practically consistent with Eq. (1) and the chaotic pulse P n will be immediately generated at the moment when X n is changed into X nþ1 .…”

Section: Resultssupporting

confidence: 79%

“…A one-dimensional map is typically implemented by periodic clock control [20,21,22,23]. In order to generate chaotic pulse sequence, we propose an ingenious design composed of edge signal forming, MM and analog switch to accomplish the iterative operation, which is shown in Fig.…”

Section: Iterative Operationmentioning

confidence: 99%

“…In past decades, the tent map, one of one-dimensional piecewise linear maps, has gained extensive attentions in applications [13,14,15], theoretical analysis [16,17,18] and circuits implementation [19,20,21,22,23]. There are current modebased and voltage mode-based approaches to implement the tent map circuits.…”

Section: Introductionmentioning

confidence: 99%

“…H. Tanaka et al [21] reported the integrated circuits of the tent map and Logistic map chaos generators based on voltage mode. A simple voltage mode-based electronic circuit consisting of five operational amplifiers, four diodes, thirteen resistors and a dc voltage source was proposed to realize the tent map in [22]. Although those circuits above are easy to implement and can generate chaotic tent map time series, chaotic pulse train may not be produced since they employ periodic clock signal to control iterative operation.…”

Section: Introductionmentioning

confidence: 99%

“…chaotic tent map time series and chaotic pulse train, are generated. Secondly, the tent map function subcircuit is realized more concisely in contrast to the existing literature ( [22] and references therein). Lastly, the resulted chaotic pulse train is controllable in terms of position and pulse interval by simply adjusting the value of variable electronic components in the circuits.…”

Section: Introductionmentioning

confidence: 99%

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A chaotic pulse sequence generator based on the tent map

Zhang

et al. 2015

IEICE Electron. Express

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A novel chaotic pulse sequence generator is presented, which includes a tent map function subcircuit and an iterative operation subcircuit. Fewer components are utilized to implement the tent map function subcircuit. Based upon boundedness of the tent map series, the iterative operation is automatically implemented through reasonable design without clock control. The method we adopt can contribute to realize the tent map as well as yield chaotic pulse train, which is controllable in terms of pulse position and pulse time interval. The results from both the test circuit and numerical simulation verify the validity of our design.

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Section: Resultssupporting

confidence: 79%

Section: Iterative Operationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A chaotic pulse sequence generator based on the tent map

Zhang

et al. 2015

IEICE Electron. Express

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FPGA simulation of chaotic tent map‐based S‐Box design

Türk

2022

Circuit Theory & Apps

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The chaotic system has a characteristically random behavior by nature, and these systems have their own characteristics in a completely deterministic structure. This feature of a chaotic system makes it difficult to predict encryptions designed based on such a system. Thanks to this unpredictable and strong feature, maps produced from chaotic systems are an important alternative in the field of encryption. One of the structures obtained by employing chaotic maps is the substitution box. S‐Box, which provides the confusion principle used in block ciphers, is the main block that dynamically replaces unencrypted data with confidential data and makes a significant contribution to ensuring high security in the encryption system. Therefore, S‐Boxes hold a critical role in block ciphers. Speed and reliability are important parameters in the creation of this main block. Especially, applications performed on hardware are more reliable and high performance. Therefore, in this study, an S‐Box was designed using field‐programmable gate arrays (FPGA) simulation from a chaotic tent map to create a fast and reliable S‐Box because FPGAs offer solutions that may be important in this field considering their fast and customizable architecture. In the proposed method, the S‐Box was created in 0.16 s. In addition, the dynamic properties of the chaotic tent map were analyzed with Lyapunov exponents, and the NIST SP 800‐22 test was applied for the information encryption suitability of the proposed chaotic system. Also, to test the reliability of the produced S‐Box structures, SAC, non‐linearity, bit independence criteria, and input/output XOR distribution table metrics were implemented. The results showed that the proposed chaotic map was dynamic and passed the reliability tests successfully.

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Synchronization and circuit simulation of a new double-wing chaos

Chen

Liu

et al. 2011

Nonlinear Dyn

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A new three-dimensional double-wing chaotic system with three quadratic terms was proposed. And the parameters which can induce the system are analyzed. The system with five equilibrium points has sophisticated dynamical behaviors and it is further investigated in details, including phase trajectory, Lyapunov exponent spectrum, Poincaré map, spectrogram map and dissipativity analysis. The circuit simulation results of the chaotic attractors are in agreement with numerical simulations. Furthermore, numerical simulations indicate that mismatch synchronization can be achieved and circuit simulations of the system synchronization are also presented.

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A simple electronic circuit realization of the tent map

Cited by 28 publications

References 10 publications

A chaotic pulse sequence generator based on the tent map

A chaotic pulse sequence generator based on the tent map

FPGA simulation of chaotic tent map‐based S‐Box design

Synchronization and circuit simulation of a new double-wing chaos

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