1. Catastrophe Theory

2. Toba catastrophe theory - Genetic bottlenecks in humans
The Toba catastrophe theory suggests that a Population bottleneck|bottleneck of the human population occurred about 70,000 years ago, reducing the total human population to around 15,000 individuals when Toba erupted and triggered a major natural environment|environmental change, including a volcanic winter

3. Catastrophe theory
In mathematics, 'catastrophe theory' is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry.

4. Catastrophe theory
Catastrophe theory, which originated with the work of the French mathematician René Thom in the 1960s, and became very popular due to the efforts of Christopher Zeeman in the 1970s, considers the special case where the long-run stable equilibrium can be identified with the minimum of a smooth, well-defined scalar potential|potential function (Lyapunov function).

5. Catastrophe theory
Small changes in certain parameters of a nonlinear system can cause equilibria to appear or disappear, or to change from attracting to repelling and vice versa, leading to large and sudden changes of the behaviour of the system. However, examined in a larger parameter space, catastrophe theory reveals that such bifurcation points tend to occur as part of well-defined qualitative geometrical structures.

6. Catastrophe theory - Elementary catastrophes
Catastrophe theory analyses degenerate critical points of the potential function — points where not just the first derivative, but one or more higher derivatives of the potential function are also zero. These are called the germ (mathematics)|germs of the catastrophe geometries. The degeneracy of these critical points can be unfolded by expanding the potential function as a Taylor series in small perturbations of the parameters.

7. Catastrophe theory - Cusp catastrophe
Zeeman, [ Catastrophe Theory], Scientific American, April 1976; pp

8. Catastrophe theory - Cusp catastrophe
Fold bifurcations and the cusp geometry are by far the most important practical consequences of catastrophe theory. They are patterns which reoccur again and again in physics, engineering and mathematical modelling.

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