Nonlinear dynamics is a branch of mathematics and physics that studies systems where changes in input do not produce proportional changes in output. This means that small alterations can lead to significant and unpredictable outcomes, making these systems complex and often chaotic. Examples include weather patterns, population growth, and the behavior of certain mechanical systems. In nonlinear dynamics, concepts like chaos theory and bifurcation are important. Chaos theory examines how tiny differences in initial conditions can result in vastly different results, while bifurcation refers to the points where a system changes its behavior dramatically. These principles help scientists understand and predict the behavior of complex systems.