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We investigate the full 5D dynamics of general braneworld models. Without making any further assumptions we show that cyclic behavior can arise naturally in a fraction of physically accepted solutions. The model does not require brane collisions, which in the stationary case remain fixed, and cyclicity takes place on the branes. We indicate that the cosmological constants play the central role for the realization of cyclic solutions and we show that its extremely small value on the observable universe makes the period of the cycles and the maximum scale factor astronomically large.
Emmanuel N. Saridakis (Sun,) studied this question.