A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The directi...

In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

A model for the transmission of dengue fever with variable human population size is analyzed. We find three threshold parameters which govern the existence of the endemic proportion equilibrium, the increase of the human population size, and the behaviour of the total number of human infectives. We prove the global asymptotic stability of the equilibrium points using the theory of competitive s...

A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The directi...

In this talk we will first describe how the clocks synchronization problem can be modeled as a consensus algorithm for heterogeneous double integrators. We show two possible implementations of this consensus based clocks synchronization. The dynamics of one of these can be described as a discrete time nonlinear system, which is a perturbation of the linear system. Hence, using the center manifo...

We investigate asymptotic behavior of polynomials $$ Q_n(z) satisfying non-Hermitian orthogonality relations $$\begin{aligned} \int _\Delta s^kQ_n(s)\rho (s)\textrm{d}s =0, \quad k\in \{0,\ldots ,n-1\}, \end{aligned}$$ where \Delta is a Chebotarëv (minimal capacity) contour connecting three non-collinear points and \rho (s) Jacobi-type weight including possible power-type singularity at the cen...

We address the problem of content replication in large distributed content delivery networks, composed of a data center assisted by many small servers with limited capabilities and located at the edge of the network. The objective is to optimize the placement of contents on the servers to offload as much as possible the data center. We model the system constituted by the small servers as a loss...

In classical electromagnetic theory, one formally defines the complex dipole moment (the electric plus ’i’ magnetic dipole) and then computes (and defines) the complex center of charge by transforming to a complex frame where the complex dipole moment vanishes. Analogously in asymptotically flat space-times it has been shown that one can determine the complex center of mass by transforming the ...

The Bremmer coupling series solution of the wave equation, in generally inhomogeneous media, requires the introduction of pseudo-differential operators. In this paper, in two dimensions, uniform asymptotic expansions of the Schwartz kernels of these operators are derived. Also, we derive a uniform asymptotic expansion of the one-way propagator appearing in the series. We focus on designing clos...

1 Glossary Almost equicontinuous CA has an equicontinuous configuration. Attractor: omega-limit of a clopen invariant set. Blocking word interrupts information flow. Closing CA: distinct asymptotic configurations have distinct images. Column subshift: columns in space-time diagrams. Cross section: one-sided inverse map. ∗Université de Nice Sophia Antipolis, Département d’Informatique, Parc Valr...