bifurcationkit / bifurcationkitdocs.jl Goto Github PK

$ grep -nr abord BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/tutorials/Swift-Hohenberg1d.md:86:               # is too big, abord continuation step
$ grep -nr agressive BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/DeflatedContinuation.md:53:- finally, you can try some agressive shift (here `0.01` in the deflation operator, like `DeflationOperator(2, dot, 0.01, [sol])` but use it wisely.
$ grep -nr algoritm BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/DeflatedContinuation.md:57:We show a quick and simple example of use. Note in particular that the algoritm is able to find the disconnected branch. The starting points are marked with crosses
$ grep -nr anlyzed BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/tutorials/cgl1dwave.md:196:We note that the branch of travelling wave solutions has a Hopf bifurcation point at which point Modulated Travelling waves will emerge. This will be anlyzed in the future.
$ grep -nr certains BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/faq.md:74:On certains cases, one can still go away with the following trick. Say one is interested (dummy example!) to study
$ grep -nr cofficients BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/tutorials/tutorials3b.md:294:A basic method for computing Floquet cofficients based on the eigenvalues of the monodromy operator is available (see [`FloquetQaD`](@ref)). It is precise enough to locate bifurcations. Their computation is triggered like in the case of a regular call to `continuation`:
$ grep -nr homogenous BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/tutorials/mittelmann.md:132:## Branch of homogenous solutions
BifurcationKitDocs.jl/docs/src/tutorials/mittelmann.md:133:At this stage, we note that the problem has a curve of homogenous (constant in space) solutions $u_h$ solving $N(\lambda, u_h)=0$. We shall compute this branch now.
BifurcationKitDocs.jl/docs/src/tutorials/mittelmann.md:143:We call `continuation` with the initial guess `sol0` which is homogenous, thereby generating homogenous solutions:
BifurcationKitDocs.jl/docs/src/tutorials/mittelmann.md:182:The second bifurcation point on the branch `br` of homogenous solutions has a 2d kernel. we provide two methods to deal with such case
BifurcationKitDocs.jl/docs/src/tutorials/mittelmann.md:248:At this stage, we know what happens at the 2d bifurcation point of the curve of homogenous solutions. We chose another method based on [Deflated problems](@ref). We want to find all nearby solutions of the problem close to this bifurcation point. This is readily done by trying several initial guesses in a brute force manner:
BifurcationKitDocs.jl/docs/src/tutorials/mittelmann.md:259:# of homogenous solutions
$ grep -nr mactch BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/faq.md:103:SciML is now able to mactch the performance of the Sundials solver `CVODE_BDF`. Check the [news](https://sciml.ai/news/2021/05/24/QNDF/) for more information.
$ grep -nr occurence BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/DeflatedContinuation.md:52:- try to limit the newton residual by using the argument `callbackN = BifurcationKit. cbMaxNorm(1e7)`. This will likely remove the occurence of `┌ Error: Same solution found for identical parameter value!!`
$ grep -nr particuliar BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/periodicOrbitTrapeze.md:81:For `:BorderedLU`, we take advantage of the bordered shape of the linear solver and use a LU decomposition to invert `dG` using a bordered linear solver. More precisely, the bordered structure of $\mathcal J$ is stored using the internal structure `POTrapJacobianBordered`. Then, $\mathcal J$ is inverted using the custom bordered linear solver `PeriodicOrbitTrapBLS` which is based on the bordering strategy (see [Bordered linear solvers (BLS)](@ref)). This particuliar solver is based on an explicit formula which only requires to invert $A_\gamma$: this is done by the linear solver `AγLinearSolver`. In a nutshell, we have:
$ grep -nr pltting BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/tutorials/cgl1dwave.md:25:# pltting utilities
$ grep -nr satifies BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/ModulatedTW.md:6:A modulated travelling wave with period $T$ satifies $q(x,t+T) = q(x-s T,t)$. Equivalently, using a moving frame to freeze the wave $\xi=x-st$, it holds that $\tilde q(\xi,t+T) = \tilde q(\xi,t)$ where $\tilde q(\xi,t):=q(\xi+st,t)$. Hence, $\tilde q$ is a periodic solution to
$ grep -nr severals BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/plotting.md:32:If you have severals branches `br1, br2`, you can plot them in the same figure by doing
$ grep -nr technics BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/tutorials/tutorialCarrier.md:10:It is a remarkably difficult problem which presents many disconnected branches which are not amenable to the classical continuation methods. We thus use the recently developed *deflated continuation method* which builds upon the Deflated Newton (see [Deflated problems](@ref)) technics to find solutions which are different from a set of already known solutions.
BifurcationKitDocs.jl/docs/src/tutorials/tutorialsCGL.md:473:We could use another way to "invert" jacobian of the functional based on bordered technics. We try to use an ILU preconditioner on the cyclic matrix $J_c$ (see [Periodic orbits based on Trapezoidal rule](@ref)) which has a smaller memory footprint:
BifurcationKitDocs.jl/docs/src/tutorials/ode/tutorialsCodim2PO.md:8:The following is a periodically forced predator-prey model studied in [^Kuznetsov] using shooting technics.
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$ grep -nr oxydation BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/tutorials/ode/tutorialCO.md:1:# CO-oxydation (codim 2)
BifurcationKitDocs.jl/docs/src/tutorials/ode/tutorialCO.md:9:model of CO-oxydation (see [^Govaerts]). The goal of the tutorial is to show a simple example of how to perform codimension 2 bifurcation detection.
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$ grep -nr catched BifurcationKitDocs.jl
BifurcationKitDocs.jl/docs/src/Predictors.md:19:This is the dumbest predictor based on the formula $(x_1,p_1) = (x_0, p_0 + ds)$ with Newton corrector ; it fails at Turning points. This is set by the algorithm `Natural()` in [`continuation`](@ref). For matrix based jacobian, it is not faster than the pseudo-arclength predictor because the factorisation of the jacobian is catched. For Matrix-free methods, this predictor can be faster than the following ones until it hits a Turning point.
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$ cat typos.sh
#!/bin/sh

sed -i "s/abord/abort/g" BifurcationKitDocs.jl/docs/src/tutorials/Swift-Hohenberg1d.md
sed -i "s/agressive/aggressive/g" BifurcationKitDocs.jl/docs/src/DeflatedContinuation.md
sed -i "s/algoritm/algorithm/g" BifurcationKitDocs.jl/docs/src/DeflatedContinuation.md
sed -i "s/anlyzed/analyzed/g" BifurcationKitDocs.jl/docs/src/tutorials/cgl1dwave.md
sed -i "s/certains/certain/g" BifurcationKitDocs.jl/docs/src/faq.md
sed -i "s/cofficients/coefficients/g" BifurcationKitDocs.jl/docs/src/tutorials/tutorials3b.md
sed -i "s/homogenous/homogeneous/g" BifurcationKitDocs.jl/docs/src/tutorials/mittelmann.md
sed -i "s/mactch/match/g" BifurcationKitDocs.jl/docs/src/faq.md
sed -i "s/occurence/occurrence/g" BifurcationKitDocs.jl/docs/src/DeflatedContinuation.md
sed -i "s/particuliar/particular/g" BifurcationKitDocs.jl/docs/src/periodicOrbitTrapeze.md
sed -i "s/pltting/plotting/g" BifurcationKitDocs.jl/docs/src/tutorials/cgl1dwave.md
sed -i "s/satifies/satisfies/g" BifurcationKitDocs.jl/docs/src/ModulatedTW.md
sed -i "s/severals/several/g" BifurcationKitDocs.jl/docs/src/plotting.md
sed -i "s/technics/techniques/g" BifurcationKitDocs.jl/docs/src/tutorials/tutorialCarrier.md
sed -i "s/technics/techniques/g" BifurcationKitDocs.jl/docs/src/tutorials/tutorialsCGL.md
sed -i "s/technics/techniques/g" BifurcationKitDocs.jl/docs/src/tutorials/ode/tutorialsCodim2PO.md
$