Unstable equilibria of some dynamical systems

Abstract

Although there are various numerical techniques to find the stable equilibria of a dynamical system in scientific computing, no widely-used computational approach has been encountered to discover the unstable equilibria of a system in the literature. This thesis aims at presenting a new approach to uncover the equilibrium positions of a dynamical system exhibiting a repelling nature. A newly developed algorithm called the reversed fixed point iteration method (RFPIM) is presented to find the unstable equilibrium positions of a nonlinear system. The current method is able to uncover the behaviour of a nonlinear system near the unstable equilibria by preserving the realistic features of the system without facing any conventional drawbacks. In this respect, it is mathematically proven and numerically observed that the present approach has various superiorities over the conventional approach.