AUTHOR=Kelley Aaron , Shilnikov Andrey 

TITLE=2θ-Burster for Rhythm-Generating Circuits

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=6

YEAR=2020

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2020.588904

DOI=10.3389/fams.2020.588904

ISSN=2297-4687

ABSTRACT=<p>We propose a minimalistic model called the <inline-formula id="inf1"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mi>θ</mml:mi></mml:mrow></mml:math></inline-formula>-burster due to two slow phase characteristics of endogenous bursters, which when coupled in 3-cell neural circuits generate a multiplicity of stable rhythmic outcomes. This model offers the benefits of simplicity for designing larger neural networks along with an acute reduction in the computation cost. We developed a dynamical system framework for explaining the existence and robustness of phase-locked states in activity patterns produced by small rhythmic neural circuits. Several 3-cell configurations, from multifunctional to monostable, are considered to demonstrate the versatility of the proposed approach, allowing the network dynamics to be reduced to the examination of 2D Poincaré return maps for the phase lags between three constituent <inline-formula id="inf2"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>2</mml:mn><mml:mi>θ</mml:mi></mml:mrow></mml:math></inline-formula>-bursters.</p>