diff --git a/docs/src/examples/gMAM_Maierstein.md b/docs/src/examples/gMAM_Maierstein.md index 6733a38c..ae12b488 100644 --- a/docs/src/examples/gMAM_Maierstein.md +++ b/docs/src/examples/gMAM_Maierstein.md @@ -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 @@ -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: diff --git a/docs/src/examples/maierstein-dynamics.png b/docs/src/examples/maierstein-dynamics.png new file mode 100644 index 00000000..2d722379 Binary files /dev/null and b/docs/src/examples/maierstein-dynamics.png differ diff --git a/src/largedeviations/sgMAM.jl b/src/largedeviations/sgMAM.jl index 6de1f67c..63718627 100644 --- a/src/largedeviations/sgMAM.jl +++ b/src/largedeviations/sgMAM.jl @@ -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(