Dynamical Systems is the branch of mathematics that attemps to understand processes in motion. Such processes occur in all branches of science. For example, the motion of the stars and the galaxies in the heavens is a dynamical system. The stock market is another system that changes in time, as is the world's weather. The changes chemicals undergo, the rise and fall of populations, and the motion of a simple pendulum are classical examples of dynamical systems in chemistry, biology, and physics.

In this lecture, we will study about example of dynamical systems, orbits, graphical analysis, fixed and periodic points, bifurcations, the quadratic family, transition to chaos, symbolic dynamics, and chaos.