Effect of Modulating Parameters in Chaos and Lyapunov Exponent

Authors

  • Monia, Ashish, Manoj Kumar, A. K. Malik

Keywords:

Chaotic map, Iterative procedure, Bifurcation plot, Lyapunov exponent.

Abstract

In the last few decades, the field of dynamics has experienced an intensive development in chaos theory. Also, it has found a celebrated place in science and engineering for solving problems of population of species, transportation models, weather forecasting, cryptography, secure communication, etc. This article deals with a simple one-dimensional map which is tested for the dynamical properties in superior fixed-point procedure. The novel system depends on the three control parameters β, r and b and exhibits a reverse representation which is shown in bifurcation and Lyapunov exponent plots. The superior recursive orbit is generated and the analytical results are derived for the fixed states and the stability of fixed states. Further, an experimental analysis is also carried out to examine the periodicity of higher orders and chaotic behavior for different ranges of parameters β, r and b = 2. Moreover, a comparative analysis between bifurcation plot and Lyapunov spectrum is also demonstrated which shows shrinkage in periodicity and chaos as the value of parameter β decreases from 1 to 0.

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Published

2022-08-04