Models of coupled population oscillators using 1-D maps

Nearest neighbour coupled systems of four 1-D oscillators

A one-dimensional (1-D) map oscillator is used to investigate the network properties of connected oscillators. The oscillators are connected as nearest neighbours, like Purkinje cells. There are two kinds of oscillators, p-type and n-type. The two types correspond to excitatory and inhibitory neurons. Thus, the 1-D oscillator network becomes an artificial system based on knowledge from the brai...

Geometric models of (d+1)-dimensional relativistic rotating oscillators

Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the energy levels and corresponding normalized energy eigenfunctions. An important property is that all these models have the same nonrelativistic limit, namely the...

Population coding by globally coupled phase oscillators

A system of globally coupled phase oscillators subject to an external input is considered as a simple model of neural circuits coding external stimulus. The information coding efficiency of the system in its asynchronous state is quantified using Fisher information. The effect of coupling and noise on the information coding efficiency in the stationary state is analyzed. The relaxation process ...

Population Dynamics of Globally Coupled Degrade-and-Fire Oscillators

Slow switching in a population of delayed pulse-coupled oscillators.

We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse couplings. By considering the stability of cluster states and symmetry possessed by our model, we argue that saddle connections between a pair of the two-cluster states are formed under general conditions. Slow switching appears as a resul...