It is a coincidence that they used the same term 'vicious cycle'.
Dr. Elaine Gottschall is talking about the vicious cycle of bacterial overgrowth in the gut and the gut's responses. She makes no mention involvement of the brain, hormones, stress etc in her ideas.
Dr. Pankaj Pasricha is talking about the brain-gut axis and GI symptoms triggered by changes in stress, hormones, neurochemicals, gut flora, etc. The changes in gut flora need not be bacterial overgrowth. They could be a decrease in certain normal bacteria, a change in the byproducts they produce when fermenting indigestible foods, a change the composition of the flora, etc.
While there is a very small overlap in ideas in the two models there is also a substantial difference between them. Both use the term vicious cycle in different ways.
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