Abstract The projection of the chaotic attractor observed from the Lorenz system in the $X$--$Z$ plane is like a butterfly, hence the classical Lorenz system is widely known as the butterfly attractor, and has served as a prototype model for studying chaotic behaviour since it was coined.In this work we take one step further to investigate some fundamental dynamic behaviours of a novel hybrid Takagi--Sugeno (TS) fuzzy Lorenz-type system, which is essentially derived from the delta-operator-based TS fuzzy modelling for complex nonlinear systems, and contains the original Lorenz system of continuous-time TS fuzzy form as a special case. By simply and appropriately tuning the additional parametric perturbations in the two-rule hybrid TS fuzzy Lorenz-type system, complex (two-wing) butterfly attractors observed from this system in the three dimensional (3D) $X$--$Y$--$Z$ space are created, which have not yet been reported in the literature, and the forming mechanism of the compound structures have been numerically investigated.
Received: 03 January 2006
Revised: 03 July 2006
Accepted manuscript online:
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