Abstract
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.
Highlights
Along with the people to deep research of the nonlinear system chaotic phenomenon and chaotic application, chaos in the electronic, communication, information processing, cranial nerve science and other areas of application has caused wide attention [1,2,3,4,5,6]
Lü et al introduced some chaotic systems which can obtain double-wing, three-wing and fourwing chaotic attractors [15,16,17,18,19], famous butterfly attractor of Lorenz equation model is a paradigm in chaos and is one of the most important models in the study of chaotic dynamics, a large number of its variants, including Chen and Lü systems with generating double-wing butterfly attractors, have been proposed and studied recently under the framework of a generalized Lorenz system family, several four-wing chaotic attractors have been obtained from the Liu system [20] and augmented Lü system [21] as well as various of their modified models, but their methods mainly depend on system simulation findings and their works don’t form a concert method, the numbers of chaotic attractors are very limited
According to the double-wing character of chaotic system, we design a parameter adjustable piecewise square function and a new stair function combining with sign function, so that the saddle-focus points of the system of index 2 are extended in the fixed y and z direction which can break the threshold limit
Summary
Along with the people to deep research of the nonlinear system chaotic phenomenon and chaotic application, chaos in the electronic, communication, information processing, cranial nerve science and other areas of application has caused wide attention [1,2,3,4,5,6]. According to the double-wing character of chaotic system, we design a parameter adjustable piecewise square function and a new stair function combining with sign function, so that the saddle-focus points of the system of index 2 are extended in the fixed y and z direction which can break the threshold limit
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