The Population Density Particle Method to Simulate Oscillator Populations

Speaker: Dr. Adam Stinchcombe

Abstract: Populations of noisy, coupled oscillators abound in all scientific
fields and provide a fertile area for mathematicians to study. To obtain
a tractable mathematical model of an oscillator population, it is common
to use dimension reduction and replace an initial model having
physically relevant variables with a phase oscillator model. This can
impede the modeler’s ability to address many scientific questions. In
this talk, I will present an analytical-numerical method that results in
a tractable model that retains the physical meaning of all variables. In
a population density approach, the density over states is tracked rather
than the individual states of all the oscillators. After accounting for
noise and coupling within the population, the population density is
governed by a non-linear and non-local integro-advection-diffusion
differential equation. I discretize this equation with a particle method
in a grid-free approach to mitigate the curse-of-dimensionality
associated with many spatial dimensions. I will introduce the approach
for a population of leaky integrate-and-fire neurons receiving noisy
input from a Poisson process. After presenting the details of the
method, I will demonstrate its use for studying the coupled oscillator
population of the suprachiasmatic nucleus, the site of the mammalian
circadian clock. The efficiency of the numerical approach enables me to
solve an optimization problem to help travelers overcome jetlag.