Complexity Study in Gumowski-Mira Map : The Use of 0-1 Test

Abstract

Gumowski-Mira map is a very interesting mathematical map which exhibits various kind of attractors-chaotic and regular. We study the behavior of some of the attractors of Gumowski-Mira map using 0-1 test used for distinguishing between periodicity, weak chaos and chaos. We demonstrate that the test is an efficient indicator as much as Lyapunov exponent as it is very easy to apply. We draw various attractors of the Gumowski-Mira map corresponding to different values of parameters. We evaluate the 0-1 test parameters in each case, and also plot the Lyapunov exponents and draw fruitful conclusions.