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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Crises in Chaotic Pendulum with Fuzzy Uncertainty

Journal of Applied Nonlinear Dynamics 4(3) (2015) 215--221 | DOI:10.5890/JAND.2015.09.001

Ling Hong; Jun Jiang; Jian-Qiao Sun

State Key Lab for Strength and Vibration, Xi’an Jiaotong University, Xi’an 710049, China

School of Engineering, University of California at Merced, Merced, CA 95344, USA

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Abstract

Crises in chaotic pendulum in the presence of fuzzy uncertainty are observed by means of the fuzzy generalized cell mapping method. A fuzzy chaotic attractor is characterized by its topology and membership distribution function. A fuzzy crisis implies a simultaneous sudden change both in the topology of a fuzzy chaotic attractor and in its membership distribution. It happens when a fuzzy chaotic attractor collides with a regular or a chaotic saddle. Two types of fuzzy crises are specified, namely, boundary and interior crises. In the case of a fuzzy boundary crisis, a fuzzy chaotic attractor disappears after a collision with a regular saddle on the basin boundary. In the case of a fuzzy interior crisis, a fuzzy chaotic attractor suddenly changes in its size after a collision with a chaotic saddle in the basin interior.

Acknowledgments

This work was supported by the Natural Science Foundation of China through the grants 11332008, 11172224, 11172223 and 11172197.

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