Study of Nonlinear Dynamics: Behaviour of Different Non Linear Systems

Abstract

Study of non linear dynamics has developed a lot in the mid 20th century and since then many scientists have contributed in this particular branch of science. In this project, the basic idea behind this branch has been studied. Lorenz attractor graph which gives us the idea of a chaotic system has been studied and obtained. Next, the phase space graphs of different non linear systems like the double pendulum and the coupled oscillator were virtually obtained. There are different phases of these systems and so are there different methods to find the state of chaos. In this report, one of those methods has been mentioned, which is the Poincare section graph. The graphs obtained help us to determine the exact state of the dynamical system. In addition, the change in the system with varying parameters has also been studied. If the initial parameters are varied, the whole system might go topsy-turvy for a particular value. This change of system with parameter gives us a particular graph known as the bifurcation diagram, from which it has been known exactly for which value of the parameter, the system changes. So overall in this dissertation, both qualitative and quantitative study of non linear systems and their corresponding dynamical behaviours has been given.