Non-linear dynamics is a branch of mathematics and physics that studies systems where changes in input do not produce proportional changes in output. Unlike linear systems, where relationships are straightforward and predictable, non-linear systems can exhibit complex behaviors such as chaos, bifurcations, and sudden shifts. These systems are often found in nature, such as in weather patterns, population dynamics, and fluid dynamics. In non-linear dynamics, small variations in initial conditions can lead to vastly different outcomes, a phenomenon often referred to as the butterfly effect. This unpredictability makes it challenging to model and understand these systems fully. Researchers use tools from chaos theory and dynamical systems theory to analyze and predict the behavior of non-linear systems.