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.
Gan J C and Xiao X C 2003 Acta Phys. Sin. 52 1085 (inChinese)
[2]
Yu J J and Xu H B 2006 Acta Phys. Sin. 55 0042 (inChinese)
[3]
Yu J J, Cao H F, Xu H B and Xu Q 2006 Acta Phys. Sin. 55 0029 (in Chinese)
[4]
Masoller C, Cavalcante Hugo L D de S and Leite J R Rios 2001 Phys. Rev. E 64 037202
[5]
Jiang M H, Shen Y, Jian J G and Liao X X 2006 Phys.Lett. A 350 221
[6]
Canovas J S, Linero A and Peralta-Salas D 2006 Physica D 218 177
[7]
Almeida J, Peralta-Salas D and Romera M 2005 Physica D 200 124
[8]
Boyarsky A, Gora P and Islam M S 2005 Physica D 210 284
[9]
Hao B L 1993 Starting with Parabolas: An Introduction toChaotic Dynamics (Shanghai: Shanghai Scientific and TechnologicalEducation Publishing House) (in Chinese)
[10]
Chen S G 1992 Mapping and Chaos (Beijing: National DefenceIndustry Press) (in Chinese)
[11]
Parker T S and Chua L O 1987 Proc. IEEE 75 982
[12]
Shimada I, Nagashima T 1979 Prog. Theor. Phys. 61 1605
YANG Zheng-Ling, WANG Wei-Wei, YIN Zhen-Xing, ZHANG Jun, CHEN Xi. Differential System's Nonlinear Behaviour of Real Nonlinear Dynamical Systems[J]. Chin. Phys. Lett., 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[J]. Chin. Phys. Lett., 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[J]. Chin. Phys. Lett., 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[J]. Chin. Phys. Lett., 2007, 24(5): 1170-1172.
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