Switching induced complex dynamics in an extended logistic map

Switching strategies have been related to the so-called Parrondian games, where the alternation of two losing games yields a winning game. We can consider two dynamics that, by themselves, yield different simple dynamical behaviors, but when alternated, yield complex trajectories. In the analysis of the alternate-extended logistic map, we observe a plethora of complex dynamic behaviors, which coexist with a super stable extinction solution.

► We consider two extensions of the logistic map that include pairing.
► For these maps extinction is a stable state that coexist with other dynamic behaviors.
► From bifurcation diagrams, we find parameters that follow the Parrondian paradox.