This paper is devoted to the analysis of a maturity structured system of hematopoietic stem cell (HSC) populations in the bone marrow. The model is a system of differential equations with several time delays. We discuss the stability of equilibria and perform the analysis of Hopf bifurcation. More precisely, we first obtain a set of improved sufficient conditions ensuring the global asymptotica...

We study time-periodic forcing of spatially extended patterns near a Turing-Hopf bifurcation point. A symmetry-based normal form analysis yields several predictions, including that (i) weak forcing near the intrinsic Hopf frequency enhances or suppresses the Turing amplitude by an amount that scales quadratically with the forcing strength, and (ii) the strongest effect is seen for forcing that ...

Folded saddle-nodes occur generically in one parameter families of singularly perturbed systems with two slow variables. We show that these folded singularities are the organizing centers for two main delay phenomena in singular perturbation problems: canards and delayed Hopf bifurcations. We combine techniques from geometric singular perturbation theory – the blow-up technique – and from delay...

We present a bifurcation analysis of a normal form for traveling waves in one-dimensional excitable media. The normal form that has been recently proposed on phenomenological grounds is given in the form of a differential delay equation. The normal form exhibits a symmetry-preserving Hopf bifurcation that may coalesce with a saddle node in a Bogdanov-Takens point, and a symmetry-breaking spatia...

The stability of a one-spike solution to a general class of reaction-diffusion (RD) system with both regular and anomalous diffusion is analyzed. The method of matched asymptotic expansions is used to construct a one-spike equilibrium solution and to derive a nonlocal eigenvalue problem (NLEP) that determines the stability of this solution on an O(1) time-scale. For a particular sub-class of th...

Internet worm attacks reduce network security and cause economic losses. The use of a quarantine strategy is prominent in defending against worms, and it has been applied to various worm propagation models. Although theoretical analysis suggests that worms must get eliminated under quarantine, such a result does not appear in a real network. The time delay considered in this paper, which is cau...

We study forms of coalgebras and Hopf algebras (i.e. coalgebras and Hopf algebras which are isomorphic after a suitable extension of the base field). We classify all forms of grouplike coalgebras according to the structure of their simple subcoalgebras. For Hopf algebras, given a W ∗-Galois field extension K ⊆ L for W a finite-dimensional semisimple Hopf algebra and a K-Hopf algebra H, we show ...

We put the known results on the antipode of a usual quasitriangular Hopf algebra into the framework of multiplier Hopf algebras. We illustrate with examples which can not be obtained by using classical Hopf algebras. The focus of the present paper lies on the class of the so-called G-cograded multiplier Hopf algebras. By doing so, we bring the results of quasitriangular Hopf group-coalgebras (a...

We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yang-Baxter equation in a systematic way. That is, the category of modules with finite cycles over a local quasitriangular Hopf algebra is a braided tensor category.

The "Sonar Hopf" cochlea is a recently much advertised engineering design of an auditory sensor. We analyze this approach based on a recent description by its inventors Hamilton, Tapson, Rapson, Jin, and van Schaik, in which they exhibit the "Sonar Hopf" model, its analysis and the corresponding hardware in detail. We identify problems in the theoretical formulation of the model and critically ...