Modeling phase synchronization of interacting neuronal populations : from phase reductions to collective behavior of oscillatory neural networks

Synchronous, coherent interaction is key for the functioning of our brain. The coordinated interplay between neurons and neural circuits allows to perceive, process and transmit information in the brain. As such, synchronization phenomena occur across all scales. The coordination of oscillatory activity between cortical regions is hypothesized to underlie the concept of phase synchronization. Accordingly, phase models have found their way into neuroscience. The concepts of neural synchrony and oscillations are introduced in Chapter 1 and linked to phase synchronization phenomena in oscillatory neural networks. Chapter 2 provides the necessary mathematical theory upon which a sound phase description builds. I outline phase reduction techniques to distill the phase dynamics from complex oscillatory networks. In Chapter 3 I apply them to networks of weakly coupled Brusselators and of Wilson-Cowan neural masses. Numerical and analytical approaches are compared against each other and their sensitivity to parameter regions and nonlinear coupling schemes is analysed. In Chapters 4 and 5 I investigate synchronization phenomena of complex phase oscillator networks. First, I study the effects of network-network interactions on the macroscopic dynamics when coupling two symmetric populations of phase oscillators. This setup is compared against a single network of oscillators whose frequencies are distributed according to a symmetric bimodal Lorentzian. Subsequently, I extend the applicability of the Ott-Antonsen ansatz to parameterdependent oscillatory systems. This allows for capturing the collective dynamics of coupled oscillators when additional parameters influence the individual dynamics. Chapter 6 draws the line to experimental data. The phase time series of resting state MEG data display large-scale brain activity at the edge of criticality. After reducing neurophysiological phase models from the underlying dynamics of Wilson-Cowan and Freeman neural masses, they are analyzed with respect to two complementary notions of critical dynamics. A general discussion and an outlook of future work are provided in the final Chapter 7.

Name dc:type.qualificationname

Ph.D.

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

Lancaster University

Year dc:date.issued

2018

Authors dc:creator

• Pietras, Bastian
• Stefanovska, Aneta
• Daffertshofer, Andreas