A complete resolution of time evolution for all species of flavylium chemical reactions network in acidic to neutral media was obtained applying Laplace transform methods, Vieta's formulae and the general partial fraction theorem. Analyses of particular systems under direct pH-jump, reverse pH-jump, stopped flow and flash photolysis experiments have been performed. The deduced formulas cover all possibilities of flavylium and anthocyanins compounds-with or without quinoidal base and with or without cis-trans isomerization barrier. The expressions for the observed rate constants in different type of experiments are quite similar. This allows creation of global procedure, based on fitting of one single set of expressions with data-set from different experiments. The mathematical approach allows easy and versatile programming.