Modified and Extended Logistic Map in Superior Orbit

Parrondo's gave a paradox, where two losing games together yields winning game when played alternatively, called as Parrondo game (a switching strategy). Rani first time studied superior iterates (i.e. superior orbit) in discrete dynamics and proves that it increases the solution domain of dynamical system. In this paper, we have studied and analyzed the stability of modified and extended logistic map for describing the dynamics of multi-scaled population (sexual reproduction) in superior orbit. We have shown that the stability of above maps is extended, and also we found some examples of “chaos1+ chaos2= order” or “undesirable1+ undesirable2= desirable” dynamic behavior in superior orbit.