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Media type:
E-Article
Title:
PERIODIC ORBITS IN PLANAR SYSTEMS MODELLING NEURAL ACTIVITY
Contributor:
KOOIJ, ROBERT E.;
GIANNAKOPOULOS, FOTIOS
imprint:
Brown University, 2000
Published in:Quarterly of Applied Mathematics
Language:
English
ISSN:
0033-569X;
1552-4485
Origination:
Footnote:
Description:
<p>In this paper we will prove certain properties of a planar dynamical system modelling the neural activity of a network consisting of two neurons. At first we show that for a certain region in parameter space (such that there exist three equilibria) the dynamical system has no periodic orbits. To this end we need a new criterion for the nonexistence of limit cycles in a system of Liénard type (Lemma 3.1). Next we derive conditions under which our model system has exactly one periodic orbit, which will be a stable limit cycle. Finally, we cover a part of the parameter space where we can prove that the dynamical system has three equilibria such that around two of the equilibria at most one limit cycle can exist.</p>