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The piecewise-linear (PWL) approximation technique developed by Julia´n et al. in the past few years is applied to find approximate models of dynamical systems dependent on given numbers of state variables and parameters. Referring to some significant examples, i.e., topological normal forms, it is shown that a PWL dynamical system approximating a given smooth system can preserve its main features. In particular, if the approximation accuracy increases, the equivalence between approximating and approximated systems shifts from qualitative to quantitative. The validity of the proposed approach is eventually tested by use of a severe nonlinear example, i.e., the Rosenzweig-MacArthur system, which describes the population dynamics in a tritrophic food chain model.