DISORDER AND CHAOS test 2 questions and answers with solutions 2025
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Module
Chaos
Institution
Chaos
Maps - ANSWER The set of all possible ORBITS under varied initial conditions.
Time is discrete (digital), gives rise to an ORBIT, and can be solved by a difference equation (iteration/substitution).
Flow - ANSWER The set of all possible TRAJECTORIES under varied initial conditions.
Time i...
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DISORDER AND CHAOS test 2 questions and
answers with solutions 2025
Maps - ANSWER The set of all possible ORBITS under varied initial conditions.
Time is discrete (digital), gives rise to an ORBIT, and can be solved by a difference equation
(iteration/substitution).
Flow - ANSWER The set of all possible TRAJECTORIES under varied initial conditions.
Time is continuous (analog), gives rise to a TRAJECTORY, and can be solved by a differential equation.
Cobweb/Staircase Diagram - ANSWER These are NOT phase space plots, but rather a method of solving a
1-d map, as exemplified by the Logistic Map.
In many cases, they permit a graphical iteration of the map (w/o the use of numbers) until the transient
behavior passes and the long range attractor can be discerned
Liouville Theorem - ANSWER The density of states in an ensemble of many identical states with different
initial conditions is constant along every trajectory in phase space.
If J = 1, the system is ... - ANSWER Hamiltonian
If J > 1, the system is ... - ANSWER Driven
If J < 1, the system is ... - ANSWER Dissipative
Logistic Map - ANSWER A way of showing the probabilities of certain outputs.
xn+1 = Rxn(1-xn)
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