Abstract
This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.
Highlights
Chaos is found to be useful or has great potential application in many disciplines
This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems
Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors
Summary
Chaos is found to be useful or has great potential application in many disciplines. 4) The system orbits are all bounded This motivates the present study on the problem of generating new chaotic attractors. Under these guidelines, though not sufficient, a new chaotic system is generated by modifying from the Lorenz system. The proposed approach in finding a new chaotic system has advantages of intuitiveness, simpleness, and convenience over some existing methods. In the rest of the paper, we use the lowercase letters x, y, z denote the state variables of the new 3D chaotic system, the uppercase letter X denotes the vector of state variables, F denotes the name of function, J denotes the Jacobian matrix, λ denotes the eigenvalue of a matrix, L denotes the Lyapunov exponents of the system
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