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Simulating memory effects with discrete dynamical systems

โœ Scribed by Jason A.C. Gallas

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
652 KB
Volume
195
Category
Article
ISSN
0378-4371

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โœฆ Synopsis

We propose using discrete dynamical systems to model non-Markovian processes. This implies a whole hierarchy of dynamical systems with dimensionality increasing proportional to the memory. Specific long-range memory effects are investigated for a quadratic, a cubic and a quartic map. Markovian processes transform the quadratic map into a normal form of the logistic equation; the H6non map corresponds to non-Markovian "first-generation" memory effects. Higher memories imply new high-dimensional systems. Non-Markovian processes imply new "memory-routes" to chaos. For the three polynomial maps discussed here it is possible to define "critical memory lengths" above which the systems essentially lose memory.

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