|
Nonlinear Dynamics: A "dynamic" is how a particular
item of interest changes over time. Nonlinear dynamics are changes
that occur over time in a nonlinear way, which is typically represented
in a graphical fashion by plots that fluctuate up and down.
Many natural phenomena are subject to nonlinear dynamics. For
instance, the population level of foxes and rabbits interact in a
nonlinear way. When fox populations are up, rabbit populations are
down, and vice versa.
The study of nonlinear dynamics is typically restricted to systems which respond
disproportionately (nonlinearly) to initial conditions or perturbing
stimuli. Nonlinear systems may exhibit chaos which is classically characterized
as sensitive dependence on initial conditions.
Chaotic systems, while distinguished from more ordered periodic
systems, are not random. When their behavior over time is appropriately
displayed (in phase space), constraints are evident which are described
by strange attractors. Phase space representations of chaotic systems,
or strange attractors, usually reveal fractal (fractals) self-similarity
across time scales.
Natural, including biological, systems often display nonlinear
dynamics and chaos.
|
