Prof. Lenka Pribylova

Masaryk University, Czech Republic



Title of the paper: Exploring Synchronization Mechanisms via Bifurcation Analysis - A Unified Approach Across Neuronal, Ecological and Physical Realms


Abstract: Synchronization mechanisms, while inherently complex, are central to a wide range of dynamical systems, from neuronal networks to physical systems like superconductive junctions. In this plenary lecture, we introduce a unified approach using the continuation program, MatCont, to explore these phenomena through the lens of bifurcation theory, specifically employing Arnold tongues and limit points of cycle manifolds on tori as analytical tools. We focus on networks of neurons connected by gap-junctions, which can be modeled as neurons excited by external alternating currents or by interconnected neurons. Whether addressing a single neuron or a complex network, our approach provides a comprehensive understanding of the possible synchronization scenarios. This methodology is also applied to shed light on bistability observed in in-phase and anti-phase synchronization patterns in neuronal networks. Our research proposes an explanation that these patterns could be linked to very high-frequency EEG signals observed near epileptic foci. While the definitive connection between these bistable synchronization patterns and very high-frequency oscillations is yet to be established, our methodology offers a promising direction for investigation, potentially contributing to a deeper understanding of pathological brain activity. Further demonstrating the applicability of our approach, we present its successful implementation in deciphering Shapiro steps in superconductive Josephson junctions and seasonal synchronization in population models. These applications underscore the power of our methodology not only in neuroscience but also in the broader context of complex dynamical systems. Through the exposition of this MatCont-based method for bifurcation analysis, we aim to inspire further utilization and development of this approach, catalyzing advancements in modeling and understanding synchronization mechanisms across a diverse range of systems.

Publications. Indexing

Publications and Indexing. Proceedings. Journals ...

Learn more

Organizing Committee. Scientific Committee.

Our Committees ...

Learn more

Submit Your Paper / Format

How to Submit your paper...

Learn more

Plenary Lectures

Plenary Lectures and Invited Lectures ...

Learn more

Special Sessions and Workshops

Special Sessions and Workshops ...

Learn more

Location and Venue

Location and Venue. How to get there ...

Learn more

Topics

Check the Topics of the conference ...

Learn more

Review process and Reviewers

About the Review Process and Reviewers ...

Learn more

Fees

Registration Fees and Deadlines ...

Learn more