Slide 12 of 25
Notes:
“Mathematical theories of dynamic systems help to explain a number of characteristics of organic development: Why certain forms are more stable than others, how the gradual growth of a system may result in sudden and radical reorganization as a new equilibrium is achieved, [and] how complex forms may be derived from their precursors.” Butterworth, 1993
Feigenbaum (1978, 1979) found that there are certain universal laws governing dynamic systems, especially their transitions from regular to chaotic behavior. The ratio of the distance between successive bifurcation values approaches a constant 4.669 as the number of bifurcations increases. This appears to be a universal property of bifurcating maps. Different equations and different mechanisms implementing those equations still show a very general universal property.
The emergence of walking is an example of a system that seems to be driven by the successive emergence of different mechanisms, but may be the result of changing dynamics. Newborn infants produce coordinated stepping movements when held upright. Movements disappear at about 2 months and reappear at about 8-10 mo. when infants begin to support their weight. Real walking emerges at about 12 mo. Could be the result of a detailed genetic blue print where one mechanism is suppressed and replaced by another (spinal vs cortical control). Thelen and Smith (1994) argue that this sequence is the result of changing dynamics. Behavior is sensitive to bodily and environmental parameters. Stepping can be elicited during the “silent” period if the baby is held upright in a warm bath. Nonstepping 7-mo. Infants perform coordinated alternating steps when held upright on a motorized treadmill. Adding weight to the legs of stepping infants stops them from stepping.
