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Using the dynamical systems approach together with the cosmographicparameters, we present a \emph{model-independent} dynamical system formulationfor cosmology in $f(R)$ gravity. The formulation is model-independent in thesense that one needs to specify not a particular functional form of $f(R)$a-priori, but rather a particular cosmological evolution, which fixes thecosmography. In a sense, our approach is the way-around the reconstructionmethod. This is shown using both non-compact and compact dynamical variables.The focus in this paper is on the compact analysis, since we demonstrate theapplicability of this formulation using examples of bouncing and cycliccosmology.

A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity