Titlebook: Hidden Dynamics; The Mathematics of S Mike R. Jeffrey Book 2018 Springer Nature Switzerland AG 2018 Sliding.Bifurcation.Discontinuity.Singu

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The Vector Field: Multipliers and Combinations,Consider a set of ordinary differential equations . or more concisely collecting the state variables .. into an .-dimensional vector . = (..,?..,?.,?..), and the functions .. into a vector . = (..,?..,?.,?..), with the derivative with respect to time . denoted by a dot.

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Linear Switching (Local Theory),In this section we take a look at systems that depend only linearly on the switching multipliers . and are therefore expressible in the form . where . is an . × . matrix. In relation to (.), the quantities in (.) are . where .. is the .. column of ..

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Breaking Determinacy,The organizing centres of local and global behaviour in smooth systems are most commonly equilibria—fixed points of a flow—or invariant manifolds emanating from equilibria. In nonsmooth systems, it turns out to be transitional points—singularities the flow passes through in finite time—that create the most interesting dynamics.