Demonstration of chaos in selected chaotic systems

Abstract

Chaos is one of the most important behavioural modes exhibited by dynamical systems and refers to the unpredictable, seemingly random, motion of trajectories of a dynamical system. In recent time, non-linear dynamics and chaos have become familiar in the technical vocabulary of most sciences and technology due to the various applications of chaos in these areas. Chaotic systems display chaotic behaviours only for specific range of values of their parameters. It is therefore important to understand the chaotic features as well as parameter values resulting in its emergence in systems. In this paper, the emergence of chaos in six chaotic systems was demonstrated using Simulink with specific initial conditions and parameter values. The simulation results obtained in form of time series illustrated noise-like waveforms which were unpredictable even after a long interval of time, while the phase portraits were irregular and sponge-like in appearance. The noise-like and unpredictable trajectories as well strange attractors observed clearly demonstrated the emergence of chaos the chosen parameter values.