Original Articles |
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Differential System's Nonlinear Behaviour of Real Nonlinear Dynamical Systems |
YANG Zheng-Ling;WANG Wei-Wei;YIN Zhen-Xing;ZHANG Jun;CHEN Xi |
School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072 |
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Cite this article: |
YANG Zheng-Ling, WANG Wei-Wei, YIN Zhen-Xing et al 2007 Chin. Phys. Lett. 24 1170-1172 |
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Abstract Chaos attractor behaviour is usually preserved if the four basic arithmetic perations, i.e. addition, subtraction, multiplication, division, or their compound, are applied. First-order differential systems of one-dimensional real discrete dynamical systems and nonautonomous real continuous-time dynamical systems are also dynamical systems and their Lyapunov exponents are kept, if they are twice differentiable. These two conclusions are shown here by the definitions of dynamical system and Lyapunov exponent. Numerical simulations support our analytical results. The conclusions can apply to higher order differential systems if their corresponding order differentials exist.
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Keywords:
05.45.Ac
05.45.Tp
89.75.Fb
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Received: 01 January 1900
Published: 23 April 2007
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PACS: |
05.45.Ac
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(Low-dimensional chaos)
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05.45.Tp
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(Time series analysis)
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89.75.Fb
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(Structures and organization in complex systems)
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