AUTHOR=Franci Alessio , Herrera-Valdez Marco Arieli , Lara-Aparicio Miguel , Padilla-Longoria Pablo 

TITLE=Synchronization, Oscillator Death, and Frequency Modulation in a Class of Biologically Inspired Coupled Oscillators

JOURNAL=Frontiers in Applied Mathematics and Statistics

VOLUME=Volume 4 - 2018

YEAR=2018

URL=https://www.frontiersin.org/journals/applied-mathematics-and-statistics/articles/10.3389/fams.2018.00051

DOI=10.3389/fams.2018.00051

ISSN=2297-4687

ABSTRACT=The general purpose of this paper is to build up on our understanding of the basic mathematical principles that underlie the emergence of biological rhythms, in particular, the circadian clock. To do so, we study the role that the coupling strength and noise play in the synchronization of a system of nonlinear, linearly coupled oscillators. First, we study a deterministic version of the model, capturing the cellular biological level, to find plausible regions in the parameter space for which synchronous oscillations in coupled pacemaker neurons emerge. Second, we focus on studying how noise and coupling interact in determining the synchronized behavior between various interacting neuronal populations, each modeling an endogenous circadian clock. To do so, we leverage the Fokker-Planck equation associated with the system. The basic mechanisms behind the generation of oscillations and the emergence of synchrony that we describe here can be used as a guide to further study coupled oscillations in biophysical nonlinear models.