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docs/src/mathematical_model.md

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# Mathematical Model
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The core of the `NetworkDynamics.jl` package is the [`Network`](@ref) function. It accepts the functions describing the
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The core of the `NetworkDynamics.jl` package is the [`Network`](
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@ref) function. It accepts the functions describing the
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local dynamics on the edges and nodes of the graph `g` as inputs, and returns a composite function compatible with the
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DifferentialEquations.jl syntax as output.
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```
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### Single Sided Edge Outputs
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In cases where a conservation law is present in a system, the edge output functions $g_\mathrm{src}$ and
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$g_\mathrm{dst}$ are not independent, but rather one of them is a function of the other. For example, in a system with
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a conservation law, the output at the source end is equal to the output at the destination end, i.e. $y_\mathrm{src} = -y_\mathrm{dst}$.
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### Single Sided Edge Outputs
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Systems exist, where the edge output functions $g_\mathrm{src}$ and $g_\mathrm{dst}$ are not independent, but rather one
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is a function of the other. For example, in a system with a flow conservation law, the flow magnitude at the
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source end is equal to the flow magnitude at the destination end (what flows in, must come out). Since the sign
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convention on both ends must be identical (e.g. positive flow is a flow towards the vertex) we get antisymmetric
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behavior: $y_\mathrm{src} = -y_\mathrm{dst}$.
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To accommodate such cases, we can use the concept of **single sided edge output functions**.
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A single sided output function only defines a function for one of the outputs:

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