Friday, March 31, 2000, Time: 14:30-15:30 / Room: HSS 2.01.12

E. Christopher Zeeman, K.B., F.R.S.

Duffing's equation: catastrophic jumps of amplitude and phase

The lecture will give an introduction to Duffing's equation, which is one of the classical oscillators first published by Duffing in 1918. It is the simplest oscillator displaying catastrophic jumps of amplitude and phase when the frequency of the forcing term is taken as a gradually changing parameter. In fact, it displays a cusp catastrophe when the nonlinearity is taken as a second parameter. The main applications have been in electronics. The lecture will demonstrate an example in mechanics and speculate on future applications in biology. For example, the brain is full of oscillators at micro level, and at macro level displays jumps in sensory perception, in psychological perception, in regulation, in switches of mood, memory, and behaviour, to say nothing of falling asleep and waking up. Partially supported by the Office of Naval Research.

MATH INFO CAL DIR CAT PP ARC LIB UTSA NBD NET SRCH MAP