Dynamic transition through JR's bifurcation

One of the fascinating aspects of brain network models (BNMs) is their ability to capture complex dynamical transitions observed in empirical brain activity. In the following plot, I explore how the Jansen-Rit model—originally designed to simulate cortical column activity—undergoes bifurcations when modulating the coupling factor that scales the weights of the structural connectivity matrix.

The role of coupling in large-scale brain dynamics

In BNMs, the coupling factor (g) determines the strength of interactions between brain regions, based on a connectivity matrix derived from diffusion MRI (here, using the AAL parcellation). As g increases, local neural populations transition from independent activity to collective dynamics, which can lead to dramatic shifts in oscillatory behavior.

The interactive visualization above demonstrates this process:

• At low g, signals generated by the model are operating in a fixed point regime.
• As g increases, long-range inputs alter both spectral properties and the temporal structure of the oscillations.
• Around critical points (bifurcations), abrupt changes in signal amplitude and coherence occur, shifting the model’s behavior into a new dynamical regime: the limit cycle.
• These transitions also influence the functional connectivity (FC) patterns, where the correlation between empirical and simulated FC varies as a function of g.

Takeaways

• The Jansen-Rit model exhibits bifurcation points as a function of structural connectivity scaling.
• Modulating g induces qualitative shifts in neural activity patterns.
• The correlation between empirical and simulated FC dynamically changes across these transitions.

I’d love to hear your thoughts—feel free to interact with the plot and share any insights or questions! 🚀