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Consider a dynamical system ẋ = f(x, k0) whose vector field is parameterized by real parameters k0. The distance-to-bifurcation problem seeks the smallest parameter variation γ = |k − k0| that results in a bifurcation of the original system's phase portrait. Prior work on this problem used numerical methods to search for the minimum γ, but these methods were computationally demanding and only guaranteed...
This paper addresses the problems of characterizing and estimating the bifurcation sets of equilibrium points in multi-parameter space of a class of nonlinear dynamical systems. Specifically, we investigate the sets of parameters that lead to saddle-node bifurcations and Hopf bifurcations at an equilibrium point of interest. First, a characterization of these sets is provided in terms of the zeros...
The Extended BP (EBP) Generalized EXIT (GEXIT) function introduced in [4] plays a fundamental role in the asymptotic analysis of sparse graph codes. For transmission over the binary erasure channel (BEC) the analytic properties of the EBP GEXIT function are relatively simple and well understood. The general case is much harder and even the existence of the curve is not known in general. We introduce...
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