Seemingly random, chaotic dynamic systems have state variables that move about in a non-periodic, bounded fashion. The sensitivity to initial conditions of chaotic signals also holds an interesting pattern. A seemingly tiny change in the values of initial conditions, can greatly affect the values of the output. This means that cross-correlation of two chaotic signals from the same source can be very low. By nature, chaotic systems are required to be non-linear and dynamic systems.The behaviour of dynamic systems was modeled using MATLAB,with pertinent non-linearities.Various mathematical aspects were studied.Since differential equations are an integral part of modeling dynamic systems, finding solutions to differential equations using MATLAB programming was also done.

Keywords: Chaos, attractors, bifurcation diagram and non-linear dynamic systems.