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GreenPrint

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I seem to be having some issues going from state space representation of a system to signal flow graph representation. My troubles seem to be, if I have something like this

[itex]\frac{d}{dt}x_{1}(t) = v_{1}(t)[/itex]

In state space representation I list functions to which the derivatives are as a function of the state space variables.

In signal flow graph model of a system am I allowed to draw transistors from one node to another node by multiplication of one in either direction?

I don't if I'm explaining this well, but if I have a node for [itex]sx_{1}(t)[/itex] and a node for [itex]v_{1}(t)[/itex] am I able to to draw the transistor arrow from the nodes in either direction since they are equal to each other? That is a arrow coming out of the node that represents [itex]sx_{1}(t)[/itex] and going into [itex]v_{1}(t)[/itex] or the arrow coming out of the node representing [itex]v_{1}(t)[/itex] and into the node representing [itex]sx_{1}(t)[/itex]. Mathematically I don't see why the direction of the arrows from the nodes can be reversed as needed since they have a one-to-one equivalency. I just want to make sure. If I'm not able to do this and I'm not sure I can solve this problem I'm trying to solve.

Thanks for any help.