Abstract
Based on the fertility data, we derive a Gauss-cosh model for autocorrelation functions in the Fourier transform space by adopting the mass-point accumulation principle of the Grassmann space to the amplitude-frequency to study the evolution of population in social problems. By using the Gauss-cosh model in the Fourier transform space, a Gauss-cos model for autocorrelation functions is suggested on time domain. The physical interpretation of the Gauss-cos model is also provided that it is a quadratic damping oscillator. Then a new algorithm is derived to approximate the autocorrelation function based on the Gauss-cos model. Numerical experiments verify that the Gauss-cos model effectively fits the autocorrelation function of the fertility rate. After analyzing the numerical results, we detect that the autocorrelation of the fertility rate is described by two major principal phases, which are caused by the public influence and the mother-daughter influence. The mother-daughter influence strongly expresses a periodic regression of the generation.
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