title: Stability of synchronous oscillations in a periodic network.
abstract: We derived a stability criterion for the totally synchronized state of a periodic network of coupled functional units. The periodicity constraint was the key assumption in deriving our circulant matrix-based stability criterion. The functional units were nonlinear discrete dynamical systems. We assumed exponentially decaying coupling strength versus distance in order to reduce the number of control parameters that would have been introduced due to the functional units' coupling. As a concrete example, we determined the stability domain of the synchronous state for logistic type functional units.
authors.affiliation: Physics and Astronomy Department, College of Charleston, Charleston, South Carolina 29424, USA. oprisans@cofc.edu
authors.forename: Sorinel Adrian
authors.initials: SA
authors.lastname: Oprisan
mesh_terms: D000465:Algorithms; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology; D017711:Nonlinear Dynamics; D010507:Periodicity; D009435:Synaptic Transmission