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docs: fix image in maierstein example
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oameye committed Dec 28, 2024
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6 changes: 3 additions & 3 deletions docs/src/examples/gMAM_Maierstein.md
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Expand Up @@ -41,7 +41,7 @@ end
sys = CoupledSDEs(meier_stein, zeros(2), (); noise_strength=σ)
```

A good reference to read about the large deviations methods is [this](https://homepages.warwick.ac.uk/staff/T.Grafke/simplified-geometric-minimum-action-method-for-the-computation-of-instantons.html) or [this]( https://homepages.warwick.ac.uk/staff/T.Grafke/simplified-geometric-minimum-action-method-for-the-computation-of-instantons.html) blog post by Tobias Grafke.
A good reference to read about the large deviations methods is [this](https://homepages.warwick.ac.uk/staff/T.Grafke/simplified-geometric-minimum-action-method-for-the-computation-of-instantons.html) or [this](https://homepages.warwick.ac.uk/staff/T.Grafke/simplified-geometric-minimum-action-method-for-the-computation-of-instantons.html) blog post by Tobias Grafke.

## Attractors

Expand Down Expand Up @@ -217,9 +217,9 @@ Large deviation theory applies principles from probability theory and statistica

For example, in a system exhibiting chaotic behavior, LDT can help quantify the probability of sudden large shifts in the system's trajectory. Similarly, in a system with multiple stable states, it can provide insight into the likelihood and pathways of transitions between these states under fluctuations. In the context of the Minimum Action Method (MAM) and the Geometric Minimum Action Method (gMAM), Large Deviation Theory is used to handle the large deviations action functional on the space of curves. This is a key part of how these methods analyze dynamical systems.

The Maier-Stein model is a typical benchmark to test such LDT techniques. Let us try to reproduce the following figure from [Tobias Grafke's blog post](https://homepages.warwick.ac.uk/staff/T.Grafke/rogue-waves-and-large-deviations.html):
The Maier-Stein model is a typical benchmark to test such LDT techniques. Let us try to reproduce the following figure from [Tobias Grafke's blog post](https://homepages.warwick.ac.uk/staff/T.Grafke/simplified-geometric-minimum-action-method-for-the-computation-of-instantons.html):

![image-2.png](attachment:image-2.png)
![maier_stein](./maierstein-dynamics.png)

Let us first make an initial path:

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3 changes: 1 addition & 2 deletions src/largedeviations/sgMAM.jl
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Expand Up @@ -38,8 +38,7 @@ relative tolerance `reltol` is achieved.
The function returns a tuple containing the final state, the action value,
the Lagrange multipliers, the momentum, and the state derivatives. The implementation is
based on the work of [Grafke et al. (2019)](
https://homepages.warwick.ac.uk/staff/T.Grafke/simplified-geometric-minimum-action-method-for-the-computation-of-instantons.html.
based on the work of [Grafke et al. (2019)](https://homepages.warwick.ac.uk/staff/T.Grafke/simplified-geometric-minimum-action-method-for-the-computation-of-instantons.html.
).
"""
function sgmam(
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