Truncation and reset process on the dynamics of Parrondo's games

The counter-intuitive feature of Parrondo's games is illustrated on various dynamical systems combined from different deterministic and stochastic subsystems. The concept of truncation and reset process is introduced, which provides a transparent perspective to understand the underlying mechanism of this class of dynamics, including the transport of flashing ratchets, and clarifies the puzzlement why random switching between two games can generate reversal dynamics as periodical switching does.