Grid multi-wing butterfly chaotic attractors generated from a new 3-D quadratic autonomous system
Xiaowen Luo
Hunan University, China
Chunhua Wang
Hunan University, China
Zhao Wan
Hunan University, China
Published 2014-04-10


a new 3-D chaotic system
Lyapunov exponent
nonlinear functions
grid multi-wing butterfly attractors

How to Cite

Luo X., Wang C. and Wan Z. (2014) “Grid multi-wing butterfly chaotic attractors generated from a new 3-D quadratic autonomous system”, Nonlinear Analysis: Modelling and Control, 19(2), pp. 272-285. doi: 10.15388/NA.2014.2.9.


Due to the dynamic characteristics of the Lorenz system, multi-wing chaotic systems are still confined in the positive half-space and fail to break the threshold limit. In this paper, a new approach for generating complex grid multi-wing attractors that can break the threshold limit via a novel nonlinear modulating function is proposed from the firstly proposed double-wing chaotic system. The proposed method is different from that of classical multi-scroll chaotic attractors generated by odd-symmetric multi-segment linear functions from Chua system. The new system is autonomous and can generate various grid multi-wing butterfly chaotic attractors without requiring any external forcing, it also can produce grid multi-wing both on the xz-plane and yz-plane. Basic properties of the new system such as dissipation property, equilibrium, stability, the Lyapunov exponent spectrum and bifurcation diagram are introduced by numerical simulation, theoretical analysis and circuit experiment, which confirm that the multi-wing attractors chaotic system has more rich and complicated chaotic dynamics. Finally, a novel module-based unified circuit is designed which provides some principles and guidelines for future circuitry design and engineering application. The circuit experimental results are consistent with the numerical simulation results. 

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