摘要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.
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.
YANG Zheng-Ling;WANG Wei-Wei;YIN Zhen-Xing;ZHANG Jun;CHEN Xi. Differential System's Nonlinear Behaviour of Real Nonlinear Dynamical Systems[J]. 中国物理快报, 2007, 24(5): 1170-1172.
YANG Zheng-Ling, WANG Wei-Wei, YIN Zhen-Xing, ZHANG Jun, CHEN Xi. Differential System's Nonlinear Behaviour of Real Nonlinear Dynamical Systems. Chin. Phys. Lett., 2007, 24(5): 1170-1172.
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