Bifurcation in infinite dimensional spaces and applications in spatiotemporal biological and chemical models

The earliest example of bifurcation is the buckling of of an elastic beam. In engineering, buckling is a failure mode characterized by a sudden failure of a structure subjected to high compressive stresses, where the actual compressive stresses at failure are greater than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to elastic instability. Bifurcation of buckling can be found in classical Euler-Bernoulli beam theory due to Leonhard Euler and Daniel Bernoulli with earlier contribution of Jacob Bernoulli. Other famous people such as Galileo Galilei, Leonardo da Vinci also have made unsuccessful attempts before the Isaac Newton invented powerful tool of differential and integral calculus [Ti, HBW].