ABSTRACT
The dynamics proposed in Chapter 3 describes trajectories through a space X × Z https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429026508/4614e5f6-5f02-45e5-afec-5950c67b94fb/content/inline-math5_265.jpg"/> whose projections in X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429026508/4614e5f6-5f02-45e5-afec-5950c67b94fb/content/inline-math5_266.jpg"/> merit special investigation: X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429026508/4614e5f6-5f02-45e5-afec-5950c67b94fb/content/inline-math5_267.jpg"/> will often be of much lower dimension than Z https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429026508/4614e5f6-5f02-45e5-afec-5950c67b94fb/content/inline-math5_268.jpg"/> , which makes it worthwhile to ask if we could restrict attention to just X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429026508/4614e5f6-5f02-45e5-afec-5950c67b94fb/content/inline-math5_269.jpg"/> . Moreover, mathematical biologists routinely discard these hidden degrees of freedom, however tacitly, and thus a general rationalisation of the procedure should be furnished if much of existing theoretical biology is to make any sense. Fortunately, such a systematic procedure is at hand, in the form of a differential inclusion. Strictly speaking, the latter only arises as a special multiple limit on the dynamics on Z https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429026508/4614e5f6-5f02-45e5-afec-5950c67b94fb/content/inline-math5_270.jpg"/> , but even where this is not warranted, the differential inclusion still gives an approximate qualitative dynamics that can serve as a useful guide to the overall topology of the dynamic flow in X https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429026508/4614e5f6-5f02-45e5-afec-5950c67b94fb/content/inline-math5_271.jpg"/> .
