In presence of unstable dimension variability numerical solutions of chaoticsystems are valid only for short periods of observation. For this reason,analytical results for systems that exhibit this phenomenon are needed. Aimingto go one step further in obtaining such results, we study the parametricevolution of unstable dimension variability in two coupled bungalow maps. Eachof these maps presents intervals of linearity that define Markov partitions,which are recovered for the coupled system in the case of synchronization.Using such partitions we find exact results for the onset of unstable dimensionvariability and for contrast measure, which quantifies the intensity of thephenomenon in terms of the stability of the periodic orbits embedded in thesynchronization subspace.
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