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<\/div>\n<\/div>\nA mathematical term for an instability or transition in a non-linear dynamical system. In such a system, it is a qualitative change in its behavior (order parameter) from one attractor state to another due to a quantitative change at some critical level (a far-from-equilibrium condition) in one or more continuously varying control parameters. Where this change takes place is referred to as the bifurcation point (see figures A-F below for an example of successive bifurcation points).<\/p>\n
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Changes from a fixed-point attractor to a chaotic attractor, via a succession of bifurcation points. When local areas in the full bifurcation diagram are magnified, the same underlying structure is revealed. In a sense then, the more things change at each bifurcation point, the more they stay the same (something referred to as ‘self-similarity’)<\/p>\n
See Attractor<\/a>, Catastrophe theory<\/a>, Chaos<\/a>, Control parameter<\/a>, Dissipative system<\/a>, Dynamical system<\/a>, Instability<\/a>, Irreversible thermodynamics<\/a>, Non-linear dynamical systems<\/a>, Order parameter<\/a>, Phase transition (or shift)<\/a>, Qualitative and quantitative change, Transition<\/p>\n <\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":" A mathematical term for an instability or transition in a non-linear dynamical system. In such a system, it is a qualitative change in its behavior (order parameter) from one attractor state to another due to a quantitative change at some critical level (a far-from-equilibrium condition) in one or more continuously varying control parameters. Where this … <\/p>\n