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We consider a general class of first-order nonlinear delay-differential equations (DDEs) with reflectional symmetry, and study completely the bifurcations of the trivial equilibrium under some generic conditions on the Taylor coefficients of the DDE. Our analysis reveals a Hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two Takens-Bogdanov point in parameter space. We compute the normal form coefficients of the reduced vector field on the centre manifold in terms of the Taylor coefficients of the original DDE, and in contrast to many previous bifurcation analyses of DDEs, we also compute the unfolding parameters in terms of these coefficients. For application purposes, this is important since one can now identify the possible asymptotic dynamics of the DDE near the bifurcation points by computing qua...
This thesis furthers our semantical understanding of polynomial time complexity by clarifying the semantical status of Lafont's soft linear logic, a logical system complete for polynomial time computation. We shall see that soft linear logic is ideal for this purpose because it possesses a very natural and simple mathematical interpretation. To begin, we introduce the notion of a multiplexor category, which is the categorical interpretation of soft linear logic. We show that a multiplexor category provides a denotational semantics for soft linear logic and that the exponential operator can be interpreted canonically as a certain type of limit. This leads to a large class of models and motivates us to introduce a new class of AJM games which we shall call noetherian. Such games may be infinite, but do not have infinite length plays (i.e...
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