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parameter, the R15 cell of the abdominal ganglion of the Aplysia demonstrates transitions between bursting and periodic modes as well as period doubling, a signatory period 3 and the Lyapounov characteristic exponent evidence (see below) for the discontinuous onset of chaos (Canavier et al, 1990). Manipulating feed back delay, the human pupillary light reflex will bifurcate into regular oscillations (Milton and Longtin, 1990). A transition between a regime of irregular discharging to oscillatory bursting behavior was induced in basal forebrain cholinergic neurons by neurotensin (Alonso et al, 1994). Sympathetic nerve discharge in decerebrate, ventilated cats demonstrated transitions between periodic, multiple periodic (quasiperiodic with changing ratios to the ventilation frequency) and subharmonic behavior in response to inferior vena cava occlusion, vagotomy, aortic constriction and spinalization (Porta et al, 1996). Period adding bifurcations were induced by changing calcium concentrations or the addition of a potassium channel blocker in the “pacemaker” formed when (rat) sciatic nerve is chronically injured (Ren et al, 1997). Changing levels of the L-type calcium channel antagonist, verapamil, alter the pattern of vasomotion of rabbit ear arteries among sets of multiple independent periods, “quasi-periodicity,” mode locking and chaos (De Brower, 1998). At critical intensity and frequency, flicker visual stimulation of the salamander generates a pharmacologically modifiable period doubling bifurcation in their ganglion cells (one spike for every two flickers) which is also seen subjectively and in occipital lobe evoked potentials at critical frequencies in bright, full-field flickered humans (Crevier and Meister, 1998).

Qualitative and Quantitative Universality in Nonlinear Dynamical Systems

“Universality” (see above) entered the parlance of physics in the context of the statistical mechanics of phase transitions near their critical points (Stanley, 1971; Stauffer, 1985; Yeomans, 1993) and has come to refer to the finite set of transitions and quantities common to nonlinear systems arising in their neighborhoods. A common physical example is the triple point of water-ice-steam on the temperature-pressure phase plane where a small change in temperature or

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