Math. Model. Nat. Phenom.
Volume 12, Number 4, 2017Complex Dynamics, Synchronization, and Emergent Behaviour in Neural Systems and Networks
|Page(s)||53 - 73|
|Published online||03 July 2017|
Analysis of an Interneuron Gamma Mechanism for Cross-Frequency Coupling
Brain and Cognition Research Unit, KU Leuven, Leuven, Belgium
2 Center for Cognitive Science, TU Kaiserslautern, Kaiserslautern, Germany
* Corresponding author. E-mail: email@example.com
Signals with multiple oscillatory components may exhibit cross frequency coupling (CFC): a slow component modulating the amplitude and/or frequency of a fast one. CFC is ubiquitous in oscillatory brain signals but how it arises has remained unclear. We recently proposed a systematic approach to simulate CFC, in which all common modulations are generated by a Neural Mass Model 7. A key mechanism in this approach is the dynamic self-feedback circuit of the fast inhibitory interneuron population that generates Gamma band oscillatory activity. Depending on noise-input level, the circuit switches between a limit cycle regime enabling amplitude modulation and a resonance regime enabling frequency modulation. In this study, we analyze the behavior of this circuit, using the describing function method for the limit cycle regime and root locus analysis for the resonance regime. The relationship between circuit parameters and behavior is investigated by bifurcation analysis.
Mathematics Subject Classification: 92B25
Key words: inhibitory interneuron / dynamic self-feedback / interneuron gamma / describing function / root locus
© EDP Sciences, 2017
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