Analysis of a new chaotic system

Journal of Systems Science & Complexity, 2008

The paper reports the dynamical study of a three-dimensional quadratic autonomous chaotic system with only two quadratic nonlinearities, which is a special case of the so-called conjugate Lü system. Basic properties of this system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagram. The analysis shows that the system has complex dynamics with some interesting characteristics in which there are several periodic regions, but each of them has quite different periodic orbits.

Journal of Bangladesh Academy of Sciences, 2012

Some fundamental properties of a chaotic three-dimensional non-linear system of the Lorenz type systems were studied. The invariance, dissipation, bifurcation and the strange attractors were investigated and analyzed one 1-scroll, two 2-scroll and two 4-scroll attractors by adding control parameters to this system. The relationship and connecting function for the 2-scroll attractor of this system were also explored. DOI: http://dx.doi.org/10.3329/jbas.v36i2.12959 Journal of Bangladesh Academy of Sciences, Vol. 36, No. 2, 159-170, 2012

In this paper, a new continuous-time four-dimensional autonomous hyper chaotic system was introduced, the new system completely different from well-Known hyper chaotic systems , the system employs ten terms include six quadratic cross-product nonlinearities terms and generate two-scroll hyper chaotic attractor at same time ,the dynamical behaviors investigated with dissipativity , symmetry , Jacobian matrix , Lyapunov Exponents, Kaplan-Yorke dimension, presence of hyper chaotic attractor and waveform analysis, where the maximum non-negative Lyapunov exponents (MLE) for system obtain as 1.9342 and Kaplan-Yorke dimension obtain as 3.0243, and the new system characteristics with ,unstable , high complexity ,and unpredictability .

2011

scirp.org

IOP Conference Series: Materials Science and Engineering, 2019

This paper reports the finding of a new three-dimensional chaotic system with four quadratic nonlinear terms. The paper starts with a detailed dynamic analysis of the properties of the system such as phase plots, Lyapunov exponents, Kaplan-Yorke dimension and equilibrium points. Our new chaotic system is obtained by modifying the dynamics of the Zhu chaotic system (2010), and it has complex chaotic properties. As an engineering application, passive control method is applied for the global chaos control of the new chaotic system. Finally, an electronic circuit implementation of the new chaotic system is designed and implemented in MultiSIM. A good qualitative agreement has been shown between the MATLAB simulations of the new chaotic system and the MultiSIM results.

Nonlinear Dynamics, 2014

This paper aim to describe a number of simplifications that can be made to the Lorenz system that preserve its dynamics as well as a number of chaotic systems. The butterfly effect was proven. The solution of differential equation and Lorenz Attractor were investigated. This study compares the dynamical behaviors of the Lorenz system with complex variables to that of the standard Lorenz system involving real variables. Different methodologies, including the Lyapunov exponents spectrum, the bifurcation diagram, the first return map to the Poincare section, topological entropy, periodic and quasi-periodic phase portraits, and chaotic behavior of the resulting system were discussed in Matlab.