Related papers: Poincare's forgotten conferences on wireless teleg…
In this paper we consider the problem of communication scheduling in wireless networks with respect to the SINR(Signal to Interference plus Noise Ratio) constraint in metric spaces. The nodes are assigned linear powers, i.e. for each sender…
Previous studies have shown that, in a diverge-merge network with two intermediate links (the DM network), the kinematic wave model always admits stationary solutions under constant boundary conditions, but periodic oscillations can develop…
A finite sequence of equidistant samples (a sample train) of a periodic signal can be identified with a point in a multi-dimensional space. Such a point depends on the sampled signal, the sampling period, and the starting time of the…
We study the number of limit cycles and the bifurcation diagram in the Poincar\'{e} sphere of a one-parameter family of planar differential equations of degree five $\dot {\bf x}=X_b({\bf x})$ which has been already considered in previous…
We consider a continuous analogue of the simulated annealing algorithm in $R^d$. We prove a convergence result, under hypotheses weaker than the usual ones. In particular, we cover cases where the gradient of the potential goes to zero at…
Experimental realization and quantitative investigation of common-noise-induced synchronization of limit-cycle oscillations subject to random telegraph signals are performed using an electronic oscillator circuit. Based on our previous…
In this paper we study the connectivity problem for wireless networks under the Signal to Interference plus Noise Ratio (SINR) model. Given a set of radio transmitters distributed in some area, we seek to build a directed strongly connected…
We present two calculations for a class of robust homoclinic cycles with symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic stability given by Krupa and Melbourne are not optimal. Firstly, we compute optimal conditions…
We show that a nonlinear dynamical system in Poincare'-Dulac normal form (in $\R^n$) can be seen as a constrained linear system; the constraints are given by the resonance conditions satisfied by the spectrum of (the linear part of) the…
Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool, which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension…
In this paper we study the reception zones of a wireless network in the SINR model with receivers that employ \emph{interference cancellation} (IC), a technique that allows a receiver to decode interfering signals, and \emph{cancel} them…
The secrecy graph is a random geometric graph which is intended to model the connectivity of wireless networks under secrecy constraints. Directed edges in the graph are present whenever a node can talk to another node securely in the…
We present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric…
This paper focuses on the Hopf bifurcation in an activator-inhibitor system without diffusion which can be modeled as a delay differential equation. The main result of this paper is the existence of the Poincar\'e-Lindstedt series to all…
Lienard systems are very important mathematical models describing oscillatory processes arising in applied sciences. In this paper, we study polynomial Lienard systems of arbitrary degree on the plane, and develop a new method to obtain a…
Due to the uncontrolled and complex real-life radio propagation environments, Claude Shannon's information theory of communications describes fundamental limits to state-of-the-art 5G radio access network (RAN) capacity, with respect to…
We show that a ring of phase oscillators coupled with transmission delays can be used as a pattern recognition system. The introduced model encodes patterns as stable periodic orbits. We present a detailed analysis of the underlying…
Understanding stickiness and power-law behavior of Poincar\'e recurrence statistics is an open problem for higher-dimensional systems, in contrast to the well-understood case of systems with two degrees-of-freedom. We study such…
We demonstrate that strongly asymmetric limit cycles can be observed in the system of three identical ring oscillators (3-gene networks known as Repressilators) globally coupled by signal molecule diffusion added to the model in a way like…
This is a survey of accumulated spectral analysis observations spanning more than a century, referring to the double layer potential integral equation, also known as Neumann-Poincar\'e operator. The very notion of spectral analysis has…