Frustration, drift, and antiphase coupling in a neural array

Abstract

Synchronization among neurons is critical for many processes in the nervous system, ranging from the processing of sensory information to the onset of pathological conditions such as epilepsy. Here, we study synchronization in an array of neurons, each modeled by a set of nonlinear ordinary differential equations. We find that an array of 20x20 coupled neurons undergoes a series of alternating low and high synchronization states, as measured by phase-locking and frequency entrainment, as the coupling constant is tuned. The role of long-range connections in inducing "small-world networks" has recently been of great interest in many physical and biological problems. Since long-range connections do exist in the brain, we investigated the role of such connections in our neural array. Introducing a biologically realistic percentage of long-range connections has no significant effect on synchronization. We find that it is rather the type of coupling and the total number of connections that determine the synchronization state of the array. We also show that some coupling conditions can lead to frustration in the system, resulting from an inability to simultaneously satisfy conflicting phase requirements. This frustration leads to a drift in the overall behavior of the network, which may offer an explanation for transitions between different types of neural oscillations observed experimentally.

Multistability, local pattern formation, and global collective firing in a small-world network of nonleaky integrate-and-fire neurons

“…in epilepsy. For the latter our findings are in line with those obtained from other modeling approaches [38][39][40][41][42][43] as well as with findings obtained from in vivo studies [44][45][46] and emphasize the need for more experimental studies on functional and structural connectivity in real neural tissue. Progress along this line can be expected from recent methodological developments [47][48][49] that allow one to study neural network activity at high spatial and temporal resolution.…”

Firing patterns and synchronization in nonsynaptic epileptiform activity: the effect of gap junctions modulated by potassium accumulation

“…Several works report on synchronization caused by an electrotonic coupling (Perez-Velazquez et al 1994, Perez-Velazquez and Carlen 2000, 2001, Galarreta and Hestrin 1999, Kepler et al 1990, Sherman and Rinzel 1991, Weihberger and Bahar 2007. The present study corroborates those results by showing burst and spike synchronization due to GJ interaction (figures 8 and 9).…”

Chimera states in a Hodgkin-Huxley model of thermally sensitive neurons

“…In each successive band of synchronized behavior, the system exhibits an additional spike per burst, moving from single spikes (region I, Fig. The observations of coupling-induced bursting are consistent with the previous observations of increased bursting behavior in coupled Huber-Braun neurons; an increased number of spikes per burst occurs in this system as the coupling constant is increased (Bahar, 2004 andWeihberger andBahar, 2007). As the control parameter T is decreased in uncoupled Huber-Braun neurons, the system exhibits a period-adding bifurcation cascade; holding T constant while sweeping the coupling constant amplitude has the effect, in essence, of recapitulating this bifurcation pattern.…”