English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

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 Lienard 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.

Periodic orbits in planar systems modelling neural activity