Bifurcation and chaos measure in some discrete dynamical systems

Abstract

Almost all natural systems have certain nonlinear properties and display ergodic and chaotic behavior during evolution when the set of parameters of such systems assume a critical set of values. So, while studying nonlinear systems with proper justification, mathematical analysis and computational skills are needed to identify the nature of chaos and the evolutionary property of any such system.

In the present work, some discrete nonlinear models have been considered and computational techniques such as  bifurcation diagrams, Lyapunov exponents, correlation dimension, topological entropy etc. have been used to identify regular and chaotic motion. The results obtained are displayed through various interesting graphics. The work also incorporates the concept of fractals and the properties of fractals. A correlation between fractals and chaos have also been discussed with proper justification.