Realization conditions for the local quasi-bursting phase in heterogeneous Rulkov lattices

Establish whether the local quasi-bursting dynamical regime at low electrical conductance is realized only in sparsely connected, local lattice topologies of electrically coupled Rulkov neurons with heterogeneous parameters, and determine the connectivity conditions under which destructive interference among many neighbors suppresses this regime.

Background

In the partially and fully heterogeneous settings, the authors observe an early decrease in the maximal Lyapunov exponent at low coupling, which they attribute to a newly identified local quasi-bursting phase: neighborhoods of individually low-frequency spiking neurons synchronize their slow oscillations, producing short periods of silence without fully entering the conventional synchronized bursting regime.

They link the existence and robustness of this phase to lattice connectivity. In more highly connected settings (e.g., next-nearest-neighbor couplings), multiple influences can cancel out, an effect they term “destructive interference,” which delays transitions and suppresses certain collective behaviors. Based on comparisons across dimensions and coupling schemes, they conjecture that local quasi-bursting may depend critically on limiting such interference in local topologies.