# Lyapunov spectrum for a user-defined dynamical system

**URL:** <https://discourse.julialang.org/t/lyapunov-spectrum-for-a-user-defined-dynamical-system/34208>\
**Category:** General Usage\
**Created:** [February 5, 2020, 2:08pm UTC](https://discourse.julialang.org/t/lyapunov-spectrum-for-a-user-defined-dynamical-system/34208 "2020-02-05T14:08:24Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![AhmedAlreweny](https://avatars.discourse-cdn.com/v4/letter/a/db5fbb/32.png) [@AhmedAlreweny](https://discourse.julialang.org/u/AhmedAlreweny)\
**Post date:** [February 5, 2020, 2:08pm UTC](https://discourse.julialang.org/t/lyapunov-spectrum-for-a-user-defined-dynamical-system/34208/1 "2020-02-05T14:08:24Z")

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Hello,  
I have seen the nice documentation [here](https://juliadynamics.github.io/DynamicalSystems.jl/latest/chaos/lyapunovs/) about calculating the Lyapunov spectrum for a dynamical system defined in `DynamicalSystems.jl` . I have a dynamical system (which is a discretized PDE) which I time-integrate using `ODEProblem` and `solve` from `DifferentialEquations.jl`. Is there a way to calculate the Lyapunov spectrum using the solution generated from the latter call?

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**Author:** ![JonasIsensee](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/jonasisensee/32/4704_2.png) [@JonasIsensee](https://discourse.julialang.org/u/JonasIsensee)\
**Post date:** [February 5, 2020, 4:15pm UTC](https://discourse.julialang.org/t/lyapunov-spectrum-for-a-user-defined-dynamical-system/34208/2 "2020-02-05T16:15:08Z")

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Hi,

I believe the intended way to do this would be to wrap your equation  
into a `ContinuousDynamicalSystem` (see [Dynamical System Definition · DynamicalSystems.jl](https://juliadynamics.github.io/DynamicalSystems.jl/latest/ds/general/) )  
and then pass it to the `lyapunovs` function.

If you need more specific arguments for the `solve` function then have a look at the advanced docs  
[https://juliadynamics.github.io/DynamicalSystems.jl/latest/advanced/](https://juliadynamics.github.io/DynamicalSystems.jl/latest/advanced/)

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**Author:** ![pafloxy](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/pafloxy/32/28694_2.png) [@pafloxy](https://discourse.julialang.org/u/pafloxy)\
**Post date:** [September 10, 2021, 9:54am UTC](https://discourse.julialang.org/t/lyapunov-spectrum-for-a-user-defined-dynamical-system/34208/3 "2021-09-10T09:54:25Z")

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Hi ! @AhmedAlreweny  
Would you mind sharing how exactly to do this? I have a custom-defined dynamical system and would like to calculate its lyapunov exponent without using the pre-defined `lyapunovs` function. Is there a way to do this within the `DifferentialEquations.jl` framework? Also I would like to do this for varying parmaters and initial conditions!