Chaos Flashcards
Examples of complex dynamics
global temperature averages, stock market fluctuations, population dynamics in laboratory blow flies
Define/explain complex dynamics
dynamics is the changes over time and natural systems often have complex dynamics/changes. complex dynamics can emerge from simple or complex causes
what is the difference in equation of logistic growth model vs. discrete logistic growth model
deltaN instead of dn/dt
deltaN = rmN(1-N/k)
Explain visual differences of continuous and discrete logistic growth models on a graph
continuous is SMOOTH and is at every instant
discrete is at certain time steps, BUMPY. look at rate of change of a population at a given time
why are population dynamics bumpy in the discrete logistic equation
because negative feedback is delayed by the interval of a time step
Define chaos
in population dynamics when the changes are unpredictable, aperiodic and bounded.
Define bifurcation diagram
a visual summary of the succession of period-doubling produced as r increases
as rm increases, bifurcations (forks) occur in shorter intervals (in shorter time from one another)
this is the onset of chaos!
Chaos/ bifurcation is extremely sensitive to… (2)
- parameter values!
ex. rm = 2.7 is much different then rm = 2.7001 with time
therefore can never calculate with exact precision - initial conditions!
ex. N0 = 0.1 vs. N0 = 0.10000001
butterfly effect = tiny changes within complex system result in impossible to predict results
What is the sea gull effect
that one flap of a sea gull’s wings would be enough to alter course of weather forever (similar to butterfly effect)
Define chaos
a trajectory is chaotic if it is bounded in magnitude, is neither periodic or approaches periodic state, and is sensitive to initial conditions
What is chaos NOT
different from randomness, it is deterministic not stochastic (but can still be difficult to distinguish from randomness)
Explain how there is no randomness in the discrete logistic equation and where the chaos comes from in relation to the equation
no randomness because have same parameter values and same initial conditions, but chaos comes from being unable to determine the parameter values and initial conditions WITH INFINITE PRECISION
What are potential consequences of chaos
if chaos is common in natural systems, won’t be able to know long term effects (ex. weather), but can still know something about predicted average conditions and extreme behaviour of the system
What evidence is there in regards to the big question: is nature chaotic?
evidence is messy
many examples for and against
Examples of reported chaos
lemmings, agrostis grass, voles, and laboratory blow flies
