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A chaotic system with Hölder continuity

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Abstract

This paper presents a new chaotic system with infinitely many equilibria. The new system contains two system parameters and a nonlinear term which does not satisfy Lipschitz continuity but does satisfy \(\frac{1}{2}\)-Hölder continuity condition. The complicated dynamics are studied through theoretical analysis and numerical simulation. Synchronization for two identical systems by a piecewise linear feedback controller is investigated based on Lyapunov stability criteria.

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Authors and Affiliations

  1. Institute of Systems Engineering, Tianjin University, Tianjin, 300072, China

    Jianxiong Zhang & Wansheng Tang

Authors
  1. Jianxiong Zhang
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  2. Wansheng Tang
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Corresponding author

Correspondence to Jianxiong Zhang.

Additional information

Supported by Research Fund for the Doctoral Program of Higher Education of China No. 20090032120034 and Tianjin University Research Foundation No. TJU-YFF-08B06.

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Zhang, J., Tang, W. A chaotic system with Hölder continuity. Nonlinear Dyn 62, 761–768 (2010). https://doi.org/10.1007/s11071-010-9760-0

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  • DOI: https://doi.org/10.1007/s11071-010-9760-0

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