COMPLEX SYSTEMS FINAL exam questions and answers with solutions 2025
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Chaos
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Chaos
fractals - ANSWER complex patterns that are similar to itself across different scales, meaning that geometrically they exist in between our familiar dimensions
ex: cantor set, koch curve, sierpinkski triangle, Mandelbrot set
self-similarity - ANSWER an object or pattern that is exactly or ap...
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COMPLEX SYSTEMS FINAL exam
questions and answers with solutions
2025
fractals - ANSWER complex patterns that are similar to itself across different scales, meaning that
geometrically they exist in between our familiar dimensions
ex: cantor set, koch curve, sierpinkski triangle, Mandelbrot set
self-similarity - ANSWER an object or pattern that is exactly or approximately similar to a part of itself.
logistical map - ANSWER the polynomial mapping that exhibits and unexpected amount of complexity
and shows how complex behavior can come from very simple non-linear dynamical equations.
geometric fractals - ANSWER fractal that is a fragmented geometric shape that can be split into parts,
each of which is a reduced-size copy of the whole figure.
natural fractals - ANSWER fractal pattern that the laws of nature repeat at different scales. Trees are a
good example, patterns that repeat smaller and smaller copies of themselves to create the biodiversity
of a forest.
algebraic fractals - ANSWER fractals that are produced by repeatedly calculating a simple equation over
and over again.
cantor set - ANSWER the set obtained from the closed interval from 0 to 1 by removing the middle third
from the interval, then the middle third from each of the two remaining sets, and continuing the process
indefinitely.
logistical equation - ANSWER A logistical equation refers to a model of population growth and is given by
the equation dPdt=rP(1−PK)
bifurcation - ANSWER the occurrence of a small smooth change made to the parameter values of a
system that causes a sudden qualitative change in its behavior
, three-body problem - ANSWER a mathematical problem of taking initial positions and velocities of three-
point masses and solving to try to figure out their subsequent motions
chaos theory - ANSWER the study of random or unpredictable behavior in systems governed by
deterministic laws and underlying patterns that are highly sensitive to initial conditions. When those
initial conditions change, even slightly, the behavior of the systems is subject to change dramatically.
Chaos theory has been used to explain irregularities in lightning, clouds, and, on another scale, in stars
and blood vessels. It helps us to understand turbulence found in all forms, including fluids. A real-life
example of chaos theory would be weather patterns because while we can usually predict weather
patterns proficiently when they are in the near future, as time goes on and more factors are added, it
becomes more difficult, practically impossible, to predict what will happen.
Laplace's Demon - ANSWER Laplace's Demon refers to the idea of determinism and the belief that the
past completely determines the future. Laplace's Demon was based on the premise of reversibility and
classical mechanics, and because many thermodynamic processes are irreversible, if thermodynamic
quantities are taken to be purely physical then no demon is possible as one could not reconstruct the
past. A real-life connection to Laplace's demon is that once these systems were finally studied in detail, a
fundamental change that ultimately overthrew the ideas of determinism began to occur in math and
science
percolation model - ANSWER The percolation model depicts the percolation theory that describes the
behavior of a network when nodes or links are removed. This is a geometric type of phase transition,
since at a critical fraction of removal the network breaks into significantly smaller connected clusters.
disinhibition model - ANSWER This model shows that in a sober state behavior is inhibited. When people
are influenced by alcohol the inhibitions are supposed to be weakened and the motivating drives are
postulated to become disinhibited and potent to influence behavior.
self-organized criticality - ANSWER A property of dynamical systems that have a critical point as an
attractor. This phenomenon is observed in certain complex systems of multiple interacting components
like neural networks, forest fires, and power grids, that produce power-law distributed avalanche sizes. It
is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and
strongly nonlinear dynamics. A real-world example of self-organized criticality would be the forest-fire
model which relates to the tendency of certain large dissipative systems to drive themselves into a
critical state independent of the initial conditions and without fine tuning of the parameters.
-sand pile
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