Examples

A gallery of copy-paste runnable examples — models, dynamics, and networks loaded from the database.

Browse runnable examples demonstrating TVBO capabilities.

  1. Linear Stability
“The simplest dynamical system is also the most fundamental: its qualitative behaviour is governed by a single number.”

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  1. 2D Phase Portraits
For two-dimensional linear systems

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  1. Saddle-Node
The saddle-node (also “fold” or “tangent”) bifurcation is the simplest codimension-1 local bifurcation:

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  1. Pitchfork
The supercritical pitchfork bifurcation:

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  1. Hysteresis (Double Saddle-Node)
A small constant tilt added to the pitchfork unfolds it into a hysteresis curve with two saddle-node bifurcations:

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  1. Hopf Normal Form
HopfNF

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Bayesian Inference of Stimulation & Excitability via tvboptim

Recover a pulse amplitude and a node’s excitability from one noisy recording, and watch the priors slide the posterior along the ridge where the two trade off.

Competing Objectives in Hopf Network Fitting via tvboptim
A delay-coupled SupHopf network is fit to two targets at once: an empirical functional connectivity (FC) matrix and a spatial peak-frequency gradient. The point is what…

Delays Shape Synchronization via tvboptim
Transmission delays organize the synchronization of a brain network of coupled phase oscillators. Because the connectome carries tract lengths, tvbo lowers the delayed…

Dynamics Database Gallery

Overview of all models in the TVBO database, organised by category.

Excitation-Inhibition Balance Tuning via tvboptim

Three ways to tune a Reduced Wong-Wang network against the same empirical FC — a feedback-inhibition loop, a combined FIC+EIB loop, and a gradient fit — compared on the…

Jansen-Rit MEG Frequency Gradient Optimization via tvboptim

Fit region-specific Jansen-Rit time constants to a cortical peak-frequency gradient, with the target derived from the connectome rather than supplied to the fit.

Load Normative Networks

Load and visualize normative brain networks from the TVBO database.

PDE Simulation
TVB-O integrates partial differential equations on a mesh with linear finite elements. The PDE backend generates a self-contained solver from a YAML experiment description…

Reduced Wong-Wang BOLD FC Optimization via tvboptim
Complete BOLD functional connectivity simulation & optimization: simulation, exploration, global and regional parameter fitting.

SC = :( sad smiley 
import numpy as np
from tvbo import Network

np.random.seed(42)
noise = np.random.uniform(0.05, 0.15, (9, 9))
np.fill_diagonal(noise, 0)  # no self-connections

# SC = :(…

Truncated Backprop-Through-Time (TBPTT) via tvboptim
Why the exact FC-loss gradient breaks past the chaos onset, and how a single integration.differentiation window fixes it. The adiabatic bifurcation envelope, the diagnostics…

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