What is a Bifurcation?
(Thanks to Zhen Mei for Contributions to this answer) A bifurcation is a qualitative change in dynamics upon a small variation in the parameters of a system. Many dynamical systems depend on parameters, e.g. Reynolds number, catalyst density, temperature, etc. Normally a gradually variation of a parameter in the system corresponds to the gradual variation of the solutions of the problem. However, there exists a large number of problems for which the number of solutions changes abruptly and the structure of solution manifolds varies dramatically when a parameter passes through some critical values. For example, the abrupt buckling of a stab when the stress is increased beyond a critical value, the onset of convection and turbulence when the flow parameters are changed, the formation of patterns in certain PDE’s, etc. This kind of phenomena is called bifurcation, i.e. a qualitative change in the behavior of solutions of a dynamics system, a partial differential equation or a delay differ
