In dynamical systems, a bifurcation occurs when a small change made to the parameter values of a system causes a sudden qualitative or topological change in its behaviour. The name “bifurcation” was first introduced by Henri Poincaré in 1885 in the first paper in mathematics showing such a behavior.
Even in simple systems such as the logistic map, bifurcations can arise and introduce chaos. A rough description of chaos is that chaotic systems exhibit a great sensitivity to initial conditions. The animation depicts a cobweb diagram of the logistic map and shows its chaotic behavior.