Non-linear and chaotic systems

A nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear dynamics, also popularly known as chaos (see Chaos Theory) is the study of systems governed by equations in which a small change in one variable can induce a large systematic change in the final state of the system. Thus, a nonlinear system exhibits very sensitive dependence on initial conditions: small or virtually unmeasurable differences in initial conditions can lead to wildly differing outcomes.

The work in the first report involves the study of the Lorenz system, popularly known for the "butterfly effect" phenomenon, the metaphorical assertion that the flapping of a butterfly’s wings can eventually cause a tornado elsewhere. The Lorenz attractor was simulated by solving the Lorenz systems of non-linear differential equations by the Runge-Kutta method. The Lorenz circuit was constructed and synchronization of chaos was achieved using Lorenz circuits which serves as a base model for secure communication using chaotic signal masking. The second report deals with Chua and Feigenbaum's circuits(double-scroll attractor and a logistic map).