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Final Paper.pdf (1.21 MB)
ETD Abstract Container
Abstract Header
Chaos and Learning in Discrete-Time Neural Networks
Author Info
Banks, Jess M
ORCID® Identifier
http://orcid.org/0000-0003-3803-1702
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1445945609
Abstract Details
Year and Degree
2015, BA, Oberlin College, Mathematics.
Abstract
We study a family of discrete-time recurrent neural network models in which the synaptic connectivity changes slowly with respect to the neuronal dynamics. The fast (neuronal) dynamics of these models display a wealth of behaviors ranging from simple convergence and oscillation to chaos, and the addition of slow (synaptic) dynamics which mimic the biological mechanisms of learning and memory induces complex multiscale dynamics which render rigorous analysis quite difficult. Nevertheless, we prove a general result on the interplay of these two dynamical timescales, demarcating a regime of parameter space within which a gradual dampening of chaotic neuronal behavior is induced by a broad class of learning rules.
Committee
Jim Walsh (Advisor)
Pages
23 p.
Subject Headings
Mathematics
;
Neurosciences
Keywords
Mathematics
;
Neuroscience
;
Computational Neuroscience
;
Chaos
;
Learning
;
Lyapunov
;
Dynamics
;
Dynamical Systems
;
Kolmogorov-Sinai Entropy
;
Hopfield Network
;
Recommended Citations
Refworks
EndNote
RIS
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Citations
Banks, J. M. (2015).
Chaos and Learning in Discrete-Time Neural Networks
[Undergraduate thesis, Oberlin College]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1445945609
APA Style (7th edition)
Banks, Jess.
Chaos and Learning in Discrete-Time Neural Networks.
2015. Oberlin College, Undergraduate thesis.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1445945609.
MLA Style (8th edition)
Banks, Jess. "Chaos and Learning in Discrete-Time Neural Networks." Undergraduate thesis, Oberlin College, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1445945609
Chicago Manual of Style (17th edition)
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Document number:
oberlin1445945609
Download Count:
374
Copyright Info
© 2015, all rights reserved.
This open access ETD is published by Oberlin College Honors Theses and OhioLINK.