Hybrid TS fuzzy modelling and simulation for chaotic Lorenz system

• 来源期刊: 中国物理（英文版）
• 关键词: Takagi-Sugeno (TS) fuzzy model chaos Lorenz system butterfly attractor
• 年，卷（期）: 2006,（11）
• 页码范围: 2541-2548
• 页数: 8页
• 语种: 英文

摘要

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.