Abstract
Chaos attractor behaviour is usually preserved if the four basic arithmetic operations,i.e. addition, subtraction, multiplication, division, or their compound,are applied. First-order differential systems of one-dimensional realdiscrete dynamical systems and nonautonomous real continuous-timedynamical systems are also dynamical systems and their Lyapunovexponents are kept, if they are twice differentiable. These twoconclusions are shown here by the definitions of dynamical system andLyapunov exponent. Numerical simulations support our analytical results.The conclusions can apply to higher order differential systems if theircorresponding order differentials exist.
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