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SUMMARY:Kimberly Ayers (Cal State San Marcos)
DTSTART:20210616T190000Z
DTEND:20210616T200000Z
DTSTAMP:20260423T024448Z
UID:GOSS2021/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GOSS2021/4/"
 >Stochastic Logistic Maps and Invariant Distributions</a>\nby Kimberly Aye
 rs (Cal State San Marcos) as part of Graduate Online Seminar Series (GOSS)
 \n\nLecture held in TBA.\n\nAbstract\nAbstract:  The logistic map\, given 
 by the mapping $f(x)=\\lambda x(1-x)$\, maps the interval $[0\,1]$ to itse
 lf when $\\lambda$ takes values between 0 and 4.  It's a famous example of
  a map that displays chaotic behavior - behavior that is seemingly without
  pattern or predictability.  One hallmark of chaos is what's known as ``se
 nsitivity to initial conditions" - two points that start arbitrarily close
  to each other will eventually have orbits that diverge from each other.  
 The deterministic logistic map has been well studied.  We are interested i
 n the \\emph{stochastic} logistic map - the map given when the $\\lambda$ 
 values take independent random values according to a distribution on $[0\,
 4]$.   Since there is a stochastic element to this map\, we can no longer 
 study the sequence of points given by taking iterates of the logistic maps
 \; the value of $f(x)$ is now a random variable\, and we study its distrib
 ution under successive iterates.  In this talk\, we'll explore what the pa
 ttern of distributions can tell us about the map\, and look for \\emph{inv
 ariant} distributions - distributions that remain fixed under successive i
 terates of the stochastic logistic map.\n
LOCATION:https://researchseminars.org/talk/GOSS2021/4/
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