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We propose a simple method of constructing a system of differential equationsof chaotic behavior based on the regression only from a scalar observabletime-series data. The estimated system enables us to reconstruct invariant setsand statistical properties as well as to infer short time-series. Oursuccessful modeling relies on the introduction of a set of Gaussian radialbasis functions to capture local structure. The proposed method is used toconstruct a system of ordinary differential equations whose orbit reconstructsa time-series of a variable of the well-known Lorenz system as a simple buttypical example. A system for a macroscopic fluid variable is also constructed.

Constructing differential equations using only a scalar time-series about continuous time chaotic dynamics