Bifurcation Theory is a branch of mathematics that studies changes in the structure of a system as parameters vary. It helps to understand how small changes in conditions can lead to sudden shifts in behavior, such as the transition from stable to chaotic states. This theory is widely applicable in fields like physics, biology, and economics. In Bifurcation Theory, a bifurcation point is where a system's equilibrium changes, leading to new solutions or behaviors. For example, in dynamical systems, a simple change in a parameter can cause a system to split into multiple paths, illustrating how complex behaviors can emerge from simple rules.