中国物理B ›› 2006, Vol. 15 ›› Issue (11): 2541-2548.doi: 10.1088/1009-1963/15/11/014

• GENERAL • 上一篇    下一篇

Hybrid TS fuzzy modelling and simulation for chaotic Lorenz system

李德权   

  1. Department of Mathematics and Physics, Anhui University of Science and Technology, Huainan 232001, China
  • 收稿日期:2006-01-03 修回日期:2006-07-03 出版日期:2006-11-20 发布日期:2006-11-20
  • 基金资助:
    Project partially supported by the Natural Science Foundation of Educational Committee of Anhui Province, China (Grant No 2006kj250B).

Hybrid TS fuzzy modelling and simulation for chaotic Lorenz system

Li De-Quan(李德权)†   

  1. Department of Mathematics and Physics, Anhui University of Science and Technology, Huainan 232001, China
  • Received:2006-01-03 Revised:2006-07-03 Online:2006-11-20 Published:2006-11-20
  • Supported by:
    Project partially supported by the Natural Science Foundation of Educational Committee of Anhui Province, China (Grant No 2006kj250B).

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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.

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.

Key words: Takagi--Sugeno (TS) fuzzy model, chaos, Lorenz system, butterfly attractor

中图分类号:  (Numerical simulations of chaotic systems)

  • 05.45.Pq
02.10.Ab (Logic and set theory) 02.30.Tb (Operator theory) 02.30.Yy (Control theory) 02.40.Pc (General topology)