A four-wing and double-wing 3D chaotic system based on sign function

Liu, Jinmei

doi:10.1016/j.ijleo.2014.08.095

Cited by 15 publications

(6 citation statements)

References 21 publications

(30 reference statements)

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“…is an unknown smooth function, a solution of the nonlinear problem (47), with the initial conditions…”

Section: Other 3d Dynamical Systems Involving a Hamilton-poisson Partmentioning

confidence: 99%

Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part

Ene,

Pop

2023

Mathematics

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The goal of this paper is to build some approximate closed-form solutions for a class of dynamical systems involving a Hamilton–Poisson part. The chaotic behaviors are neglected. These solutions are obtained by means of a new version of the optimal parametric iteration method (OPIM), namely, the modified optimal parametric iteration method (mOPIM). The effect of the physical parameters is investigated. The Hamilton–Poisson part of the dynamical systems is reduced to a second-order nonlinear differential equation, which is analytically solved by the mOPIM procedure. A comparison between the approximate analytical solution obtained with mOPIM, the analytical solution obtained with the iterative method, and the corresponding numerical solution is presented. The mOPIM technique has more advantages, such as the convergence control (in the sense that the residual functions are smaller than 1), the efficiency, the writing of the solutions in an effective form, and the nonexistence of small parameters. The accuracy of the analytical and corresponding numerical results is illustrated by graphical and tabular representations. The same procedure could be successfully applied to more dynamical systems.

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“…is an unknown smooth function, a solution of the nonlinear problem (47), with the initial conditions…”

Section: Other 3d Dynamical Systems Involving a Hamilton-poisson Partmentioning

confidence: 99%

Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part

Ene,

Pop

2023

Mathematics

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show abstract

“…According to the piecewise linear function (11) and equation (14), we can choose 16 = 12 kΩ, 17 = 2 kΩ, 18 = 1 kΩ, and 19 = 14 kΩ.…”

Section: Journal Of Electrical and Computer Engineeringmentioning

confidence: 99%

“…Since Lorenz found the first chaotic model in 1963 [1], people have had a great interest to construct the chaotic attractors with different shape and quantity. At present, the existing chaotic attractors could be divided into two types: the multiscroll chaotic attractors (including double-scroll [2], multiscroll [3,4], gird multi-scroll [5], and multi-directional multiscroll chaotic attractors [6]) and the multi-wing butterfly chaotic attractors (containing two-wing [7][8][9][10][11], four-wing [12][13][14][15][16], multi-wing [17][18][19][20], and grid multi-wing [21,22] butterfly chaotic attractors). The approach had grown pretty mature constructing multi-scroll chaotic attractors.…”

Section: Introductionmentioning

confidence: 99%

A Novel Method for Constructing Grid Multi-Wing Butterfly Chaotic Attractors via Nonlinear Coupling Control

Huang

2016

Journal of Electrical and Computer Engineering

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A new method is presented to construct grid multi-wing butterfly chaotic attractors. Based on the three-dimensional Lorenz system, two first-order differential equations are added along with one linear coupling controller, respectively. And a piecewise linear function, which is taken into the linear coupling controller, is designed to form a nonlinear coupling controller; thus a five-dimensional chaotic system is produced, which is able to generate gird multi-wing butterfly chaotic attractors. Through the analysis of the equilibrium points, Lyapunov exponent spectrums, bifurcation diagrams, and Poincaré mapping in this system, the chaotic characteristic of the system is verified. Apart from the research above, an electronic circuit is designed to implement the system. The circuit experimental results are in accordance with the results of numerical simulation, which verify the availability and feasibility of this method.

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“…In Ref. [14], Liu successfully designed a special 3D four-wing system by introducing sign function. By virtue of turning a third-order system into a fourth-order system with the choice of memristor, Yu et al proposed a high-order fourth-wing hyperchaotic system [15].…”

Section: Introductionmentioning

confidence: 99%

A Novel Six-Wing Chaotic System with Line Equilibrium and its Application in Image Encryption

Xia

Fan

et al. 2023

Preprint

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This brief introduces a novel chaotic system with line equilibrium, which has six wings. The dynamic properties of the system, including chaos, period-doubling bifurcation, and coexisting attractors have been verified by analysis tools such as phase diagram, bifurcation diagram, Poincare map and Lyapunov exponents (LEs). Different kinds of attractors are obtained by controlling one parameter. Especially, offset boosting control and sensitivity to initial values are discovered. In addition, two positive LEs are observed when a parameter is fixed. Emulated by Multisim, the consistency of analog circuit and numerical simulation confirms the feasibility of the theoretical model of the new system. The proposed system is applied to image encryption based on classical algorithm, it is histogram, adjacent pixel correlation, attack resistance, and information entropy can be verified, and the experimental results show that the new system is very sensitive to key and plaintext and can effectively resist statistical and differential attacks.

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A four-wing and double-wing 3D chaotic system based on sign function

Cited by 15 publications

References 21 publications

Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part

Approximate Closed-Form Solutions for a Class of 3D Dynamical Systems Involving a Hamilton–Poisson Part

A Novel Method for Constructing Grid Multi-Wing Butterfly Chaotic Attractors via Nonlinear Coupling Control

A Novel Six-Wing Chaotic System with Line Equilibrium and its Application in Image Encryption

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