A Novel Fourth-Order Chaotic Circuit and Its Implementation

2008 ◽  
Author(s):  
Zhusong Liu ◽  
Simin Yu ◽  
Guobo Xie ◽  
Yijun Liu
Keyword(s):  
Fourth Order ◽  
Chaotic Circuit

Analysis, circuit implementation and applications of a novel chaotic system

Circuit World ◽  
2017 ◽  
Vol 43 (3) ◽  
pp. 118-130 ◽  
Author(s):  
Li Xiong ◽  
Zhenlai Liu ◽  
Xinguo Zhang
Keyword(s):  
Chaotic System ◽  
Fourth Order ◽  
Secure Communication ◽  
Phase Portraits ◽  
The Novel ◽  
Circuit Implementation ◽  
Chaotic Circuit ◽  
Third Order ◽  
Content Type ◽  
Chaotic Secure Communication

Purpose Lack of optimization and improvement on experimental circuits precludes comprehensive statements. It is a deficiency of the existing chaotic circuit technology. One of the aims of this paper is to solve the above mentioned problems. Another purpose of this paper is to construct a 10 + 4-type chaotic secure communication circuit based on the proposed third-order 4 + 2-type circuit which can output chaotic phase portraits with high accuracy and high stability. Design/methodology/approach In Section 2 of this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new third-order Lorenz-like chaotic system is proposed based on the 4 + 2 circuit. Then some simulations are presented to verify that the proposed system is chaotic by using Multisim software. In Section 3, a fourth-order chaotic circuit is proposed on the basis of the third-order 4 + 2 chaotic circuit. In Section 4, the circuit design method of this paper is applied to chaotic synchronization and secure communication. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. In Section 5, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented in an analog electronic circuit. The analog circuit implementation results match the Multisim results. Findings The simulation results show that the proposed fourth-order chaotic circuit can output six phase portraits, and it can output a stable fourth-order double-vortex chaotic signal. A new 10 + 4-type chaotic secure communication circuit is proposed based on the novel third-order 4 + 2 circuit. The scheme has the advantages of clear thinking, efficient and high practicability. The experimental results show that the precision is improved by 2-3 orders of magnitude. Signal-to-noise ratio meets the requirements of engineering design. It provides certain theoretical and technical bases for the realization of a large-scale integrated circuit with a memristor. The proposed circuit design method can also be used in other chaotic systems. Originality/value In this paper, a novel third-order 4 + 2 chaotic circuit is constructed and a new chaotic system is proposed on the basis of the 4 + 2 chaotic circuit for the first time. Some simulations are presented to verify its chaotic characteristics by Multisim. Then the novel third-order 4 + 2 chaotic circuit is applied to construct a fourth-order chaotic circuit. Simulation results verify the existence of the new fourth-order chaotic system. Moreover, a new 10 + 4-type chaotic secure communication circuit is proposed based on chaotic synchronization of the novel third-order 4 + 2 circuit. To illustrate the effectiveness of the proposed scheme, the intensity limit and stability of the transmitted signal, the characteristic of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. Finally, the proposed third-order 4 + 2 chaotic circuit and the fourth-order chaotic circuit are implemented through an analog electronic circuit, which are characterized by their high accuracy and good robustness. The analog circuit implementation results match the Multisim results.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

Exploring the Fourth Order

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Barend KLITSIE ◽  
Rebecca PRICE ◽  
Christine DE LILLE
Keyword(s):  
Action Research ◽  
Fourth Order ◽  
Subject Matter ◽  
Action Research Project ◽  
Research Project ◽  
Building Trust ◽  
Current Business

Companies are organised to fulfil two distinctive functions: efficient and resilient exploitation of current business and parallel exploration of new possibilities. For the latter, companies require strong organisational infrastructure such as team compositions and functional structures to ensure exploration remains effective. This paper explores the potential for designing organisational infrastructure to be part of fourth order subject matter. In particular, it explores how organisational infrastructure could be designed in the context of an exploratory unit, operating in a large heritage airline. This paper leverages insights from a long-term action research project and finds that building trust and shared frames are crucial to designing infrastructure that affords the greater explorative agenda of an organisation.

Normal form method in search for periodic solutions of ordinary differential equations. Case of the fourth order

2018 ◽  
pp. 24-34
Author(s):  
V. F. Edneral ◽  
O. D. Timofeevskaya
Keyword(s):  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Numerical Calculations ◽  
Computational Time ◽  
Resonant Normal Form ◽  
Normal Form Method

Introduction:The method of resonant normal form is based on reducing a system of nonlinear ordinary differential equations to a simpler form, easier to explore. Moreover, for a number of autonomous nonlinear problems, it is possible to obtain explicit formulas which approximate numerical calculations of families of their periodic solutions. Replacing numerical calculations with their precalculated formulas leads to significant savings in computational time. Similar calculations were made earlier, but their accuracy was insufficient, and their complexity was very high.Purpose:Application of the resonant normal form method and a software package developed for these purposes to fourth-order systems in order to increase the calculation speed.Results:It has been shown that with the help of a single algorithm it is possible to study equations of high orders (4th and higher). Comparing the tabulation of the obtained formulas with the numerical solutions of the corresponding equations shows good quantitative agreement. Moreover, the speed of calculation by prepared approximating formulas is orders of magnitude greater than the numerical calculation speed. The obtained approximations can also be successfully applied to unstable solutions. For example, in the Henon — Heyles system, periodic solutions are surrounded by chaotic solutions and, when numerically integrated, the algorithms are often unstable on them.Practical relevance:The developed approach can be used in the simulation of physical and biological systems.

Dynamic analysis of a helical gear reduction by experimental and numerical methods

2020 ◽  
Vol 68 (1) ◽  
pp. 48-58
Author(s):  
Chao Liu ◽  
Zongde Fang ◽  
Fang Guo ◽  
Long Xiang ◽  
Yabin Guan ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Numerical Models ◽  
Helical Gear ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Lumped Mass ◽  
Gear Mesh

Presented in this study is investigation of dynamic behavior of a helical gear reduction by experimental and numerical methods. A closed-loop test rig is designed to measure vibrations of the example system, and the basic principle as well as relevant signal processing method is introduced. A hybrid user-defined element model is established to predict relative vibration acceleration at the gear mesh in a direction normal to contact surfaces. The other two numerical models are also constructed by lumped mass method and contact FEM to compare with the previous model in terms of dynamic responses of the system. First, the experiment data demonstrate that the loaded transmission error calculated by LTCA method is generally acceptable and that the assumption ignoring the tooth backlash is valid under the conditions of large loads. Second, under the common operating conditions, the system vibrations obtained by the experimental and numerical methods primarily occur at the first fourth-order meshing frequencies and that the maximum vibration amplitude, for each method, appears on the fourth-order meshing frequency. Moreover, root-mean-square (RMS) value of the acceleration increases with the increasing loads. Finally, according to the comparison of the simulation results, the variation tendencies of the RMS value along with input rotational speed agree well and that the frequencies where the resonances occur keep coincident generally. With summaries of merit and demerit, application of each numerical method is suggested for dynamic analysis of cylindrical gear system, which aids designers for desirable dynamic behavior of the system and better solutions to engineering problems.

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