This unique addition to reference literature provides an introduction to the major concepts and contemporary issues that are essential for students of environmental science and environmental studies to know. With over 200 entries authored by world-class names like Anthony Brazel, John Day and Edward Keller, this text is divided into six sections: Environmental Science, Environments, Paradigms & Concepts, Processes & Dynamics, Scales & Techniques, and Environmental Issues.
A series of mathematical forumulations which can be used to account for sudden shifts of a system from one state to another as a result of the system being moved across a threshold condition. In mathematics, catastrophe theory was introduced in the 1960s by Rene Thorn (1923–) to signify those sudden changes, or jumps, which occur after relatively smooth progress. Such sudden shifts in behaviour arising from small changes in circumstances, constitute a special branch of dynamical systems theory. Catastrophe theory is generally considered as a branch of geometry because the variables and resultant behaviour are usefully depicted as curves or surfaces, with seven fundamental types, with the names that Thorn suggested (fold catastrophe, cusp catastrophe, swallowtail catastrophe, butterfly catastrophe, hyperbolic umbilic ...