Analysis and circuit implementation of fractional order multi-wing hidden attractors. (English) Zbl 1490.94079
Summary: In order to improve the complexity of chaotic signals, a new three-dimensional quadratic two-wing hidden chaotic system is proposed in this paper, the corresponding fractional order multi-wing system is put forward. Fractional order multi-wing chaotic hidden attractors are generated in the system. The Adomian decomposition algorithm is used to solve the proposed fractional-order chaotic system, the complex chaotic map, Lyaponov exponent spectrum, bifurcation diagram, Poincaré section, power spectrum, power spectrum Shannon entropy and exponential entropy, SE (spectral entropy) complexity are obtained, and the dynamic characteristics of the system are analyzed. Also, the riddled basins of attraction and coexisting multi-stable patterns are studied. By designing the equivalent circuit module of fractional integral operator, a circuit system for the fractional-order chaotic system is constructed and the 0.9-order multi-wing chaotic attractors are realized.
MSC:
| 94C05 | Analytic circuit theory |
| 94C60 | Circuits in qualitative investigation and simulation of models |
| 94A17 | Measures of information, entropy |
| 26A33 | Fractional derivatives and integrals |
| 37N35 | Dynamical systems in control |
Keywords:
fractional order multi-wing hidden attractor; SE complexity; Shannon entropy; riddled basins; circuit realizationReferences:
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