Seasonality as a Parrondian Game in the Superior Orbit

Abstract

In ecological modeling, switching strategy is used to represent seasonality, i.e., different environmental conditions. Switching strategies is also known as Parrondo’s paradox, where the alternation of two losing games combined in deterministic and random manner yields a winning game, i.e., in game theory “lose + lose = win”, in ecological systems “undesirable + undesirable = desirable” and in a dynamical system “chaos + chaos = order”. The logistic map \(f(x) = rx(1 - x),x \in [0,1]\)shows different forms by taking 0 3.57, but after iterating it in superior orbit it is extended to 21. But still chaotic range exists, i.e., in ecological system some undesirable behaviors are observed. In this paper, we consider a winter season and summer season in superior orbit and both will derive the population towards the chaos or undesirable individually and also the case of extinction and chaotic, but after applying switching strategy to them they are ordered or desirable “undesirable + undesirable = desirable”. And also, we have considered a four-season model, to study either migration or immigration. Further, we have studied a noisy switching strategy for the above case and shown that desirable oscillatory behavior still prevails.