👉 Bifurcations are a mathematical concept in dynamical systems and chaos theory that describe how solutions to initial value problems for differential equations evolve over time. They occur when an equilibrium point of one equation is approached from different directions, leading to a number of local minima or maxima that cannot be reached by the system without additional conditions. Bifurcations are crucial in understanding the behavior of dynamical systems and have been used as a tool for studying complex systems such as biological systems,