The Significance of Limit Cycles in a Neural Model with Poisson and Gauss Connectivity

Abstract

Isolatedrandomly interconnected nets with chemical markers and noise are investigated, which follow Poisson or Gauss distribution. The obtained results reveal limit cycles. The Poisson limit cycles are primarily large and complex, while the Gauss ones are regularly small.The Poisson limit cycles have various types depending on the shape andtime ofthe transient part, whereas the Gauss ones have the same form, plain, with no particular types of the transient component and are small. The epilepticMEGs follow Poisson distributions with high magnetic amplitudes varying with time and repeatable at time intervals with similar characteristics like the limit cycles. Alternatively the MEGs from healthy subjects have Gauss distributions. The above mentioned differentiations are due to the fact that in Poisson distributed connectivity the activity of the system is organized and synchronized as in epileptic discharges while in Gauss one is random and disordered as in healthy subjects. Limit cycles have been used to form the behavior of many oscillatory systems.