Dale Tuggy's Stanford Encyclopedia of Philosophy entry, Trinity, provides a good overview. The specialist blog, Trinities, to which he contributes will also be of interest. Here is Richard Cartwright's excellent "On the Logical Problem of the Trinity." Caveat lector: it contains a few scanning errors. Essential reading nonetheless. Cartwright rejects Peter Geach's relative identity solution. For a defense of the relative identity approach, see A, P. Martinich, Identity and Trinity. (Requires access to JSTOR. What? You say you don't have access to JSTOR? How do you live without it?)
Jeffrey Brouwer and Michael Rea, Material Constitution and the Trinity. For William Lane Craig's critique, see Does the Problem of Material Constitution Illuminate The Doctrine of The Trinity?
That barely scratches the surface, but should keep you busy for a while.
By the way, don't confuse the diagram with the doctrine. It is a graphic 'aid' which probably does more harm than good. Philosophical thinking is not picture-thinking. As Hegel might have said, Philosophisches Denken ist nicht vorstellendes, sondern begriffliches, Denken.
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