Desynchronization Dynamics of Two Coupled Oscillators

The two neurons are initially uncoupled and synchronized. When uncoupled, each neuron is a two-dimensional system described by a voltage () and a recovery variable (), the latter of which describes the extent to which a neuron can change its voltage in time. Equilibrium points for this system are defined by the intersection of two nullclines in two-dimensional state space. Since the two neurons begin in synchronous oscillation, a limit cycle exists about the equilibrium point. The neurons may be coupled by two coupling constants, which may be either positive (excitatory) or negative (inhibitory). One of the neurons also receives an external current input. In this case, the state space for each neuron becomes three-dimensional. Only one nullcline, a cubic surface, is shown, with the trajectory of each oscillator also plotted. Interesting dynamics can be seen by varying the coupling constants, input current, and time of the trajectory. Certain attractors of the system include multiple limit cycles, stable fixed-nodes, and sometimes even chaotic dynamics.