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Update docs/src/catalyst_applications/dynamical_systems.md
Co-authored-by: George Datseris <[email protected]>
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docs/src/catalyst_applications/dynamical_systems.md

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# [Analysing model steady state properties with DynamicalSystems.jl](@id dynamical_systems)
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The [DynamicalSystems.jl package](https://github.com/JuliaDynamics/DynamicalSystems.jl) implements a wide range of methods for analysing dynamical systems. This includes both continuous-time systems (i.e. ODEs) and discrete-times ones (difference equations, these are, however, not relevant to chemical reaction network modelling). For ODEs, methods primarily include those for analysing a system's steady state and stability properties. Here we give two examples of how DynamicalSystems.jl can be used, with the package's [documentation describing many more features](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). Finally, it should also be noted that DynamicalSystems.jl contain several tools for [analysing data measured from dynamical systems](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/contents/#Exported-submodules).
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The [DynamicalSystems.jl package](https://github.com/JuliaDynamics/DynamicalSystems.jl) implements a wide range of methods for analysing dynamical systems. This includes both continuous-time systems (i.e. ODEs) and discrete-times ones (difference equations, these are, however, not relevant to chemical reaction network modelling). Here we give two examples of how DynamicalSystems.jl can be used, with the package's [documentation describing many more features](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/tutorial/). Finally, it should also be noted that DynamicalSystems.jl contain several tools for [analysing data measured from dynamical systems](https://juliadynamics.github.io/DynamicalSystemsDocs.jl/dynamicalsystems/dev/contents/#Exported-submodules).
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## [Finding basins of attraction](@id dynamical_systems_basins_of_attraction)
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Given enough time, an ODE will eventually reach a so-called [*attractor*](https://en.wikipedia.org/wiki/Attractor). For chemical reaction networks (CRNs), this will (almost always) be either a *steady state* or a *limit cycle*. Since ODEs are deterministic, which attractor a simulation will reach is uniquely determined by the initial condition (assuming parameter values are fixed). Conversely, each attractor is associated with a set of initial conditions such that model simulations originating in these will tend to that attractor. These sets are called *basins of attraction*. Here, phase space (the space of all possible states of the system) can be divided into a number of basins of attraction equal to the number of attractors.

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