| 摘要 |
PROBLEM TO BE SOLVED: To identify and predict main time series data of strong nonlinearity by introducing the nonlinear differential equation of two-dimensional two variables one of which expresses a main variable and the other of which expresses an auxiliary variable, identifying main time series data and predicting main time series data. SOLUTION: Two kinds of main time series data are inputted (200). Next, the nonlinear differential equation expressing the main variable and the auxiliary variable is introduced like dx/dt=r[(1-x/k)-ky/(x+d)]x, dx-dt=s(1-y/γx)y, e.g. (201). In this example, (x) is given the identification (202) and the prediction (203) of main time series data by using a limit cycle. In order to especially controlling amplitude at the time of solving the nonlinear differential equation, variable transformation is executed like next. u=(1-μ)x*+μx, v=(1-ν)y*+νy, but x*, y*: value of a balancing point, μ, ν: a parameter (μ, ν>0). In addition, a parameter is fixed to finely adjust the parameter so as to improve the degree of applying in addition from there. |
