Dynamic analysis of a chaotic system

Su, Kalin

doi:10.1016/j.ijleo.2015.09.052

Cited by 8 publications

(4 citation statements)

References 21 publications

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“…Figures 19 and 20 show that the two systems are synchronized and the state errors converge to zero exponentially, which proved the effectiveness of the designed control functions to synchronize the proposed snail-shaped chaotic system (1) and the hyperchaotic system of Rossler (15). ( 23) 19 Coordinates times series of the master and the slave systems…”

Section: Numerical Simulation Resultsmentioning

confidence: 79%

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A snail-shaped chaotic system with large bandwidth: dynamical analysis, synchronization and secure communication scheme

2020

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In this paper, a snail-shaped chaotic system with large bandwidth is first introduced, it contains two quadratic, one cubic and two quartic nonlinear terms. The new snail-shaped autonomous system can exhibit periodic, quasi-periodic and chaotic behaviors with the variations of its parameters. The major properties of the proposed model are discussed using equilibrium points, Kaplan-Yorke dimension, Lyapunov exponents spectrum and bifurcation diagrams. The feasibility of the snail-shaped system is verified by implementing an electronic circuit via Multisim software. The obtained results proving the complex chaotic behavior of the new system, which make it very desirable to use in many fields of engineering especially in secure communication. Also, synchronization between the snail-shaped chaotic system and the Rossler hyperchaotic system is achieved. Finally, a new simple secure communication scheme is developed based on the proposed system and using drive response synchronization in order to prove the success of the new system to complete the encryption/decryption process.

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Section: Numerical Simulation Resultsmentioning

confidence: 79%

“…The parameters values as in ( 2) and the initial conditions [20, −7, 0.2, 0.2 ] are chosen for the proposed system (1) and the parameters values as in ( 16) and the initial conditions [14, 2, −17, 7] are chosen for the Rossler system (15).…”

Section: Numerical Simulation Resultsmentioning

confidence: 99%

A snail-shaped chaotic system with large bandwidth: dynamical analysis, synchronization and secure communication scheme

2020

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“…Varan et al [11] implemented a synchronization circuit model of a third-degree Malasoma system with chaotic flow. Su [12] investigated the horseshoe chaos using the topological horseshoe theory, taking into account a three-dimensional (3D) autonomous chaotic system. Zhou et al [13] introduced and analyzed theoretically the basic dynamical properties of a three-dimensional chaotic system.…”

Section: Introductionmentioning

confidence: 99%

“…The approximate analytic solution ūmOPIM (77) of Equation(12) and the corresponding numerical solution for a = −0.15, the initial conditions x 0 = 0.25, y 0 = 0.55, z 0 = 1.5, and N max = 25 (absolute errors: u = |u numerical − ūmOPIM |).…”

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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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A more chaotic and easily hardware implementable new 3-D chaotic system in comparison with 50 reported systems

Singh

Roy

2018

Nonlinear Dyn

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Dynamic analysis of a chaotic system

Cited by 8 publications

References 21 publications

A snail-shaped chaotic system with large bandwidth: dynamical analysis, synchronization and secure communication scheme

A snail-shaped chaotic system with large bandwidth: dynamical analysis, synchronization and secure communication scheme

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

A more chaotic and easily hardware implementable new 3-D chaotic system in comparison with 50 reported systems

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