相关论文: Limit directions of a vector cocycle, remarks and …

We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate…

After the fundamental work of Livschitz in [1; 2], various research directions emerged, among which the following stand out: (i) the study of cocycles with values in groups and semigroups beyond R, as well as the investigation of…

Additive noise is known to produce counter-intuitive behaviors in nonlinear dynamical systems. Previously, it was shown that systems with a deterministic limit cycle can display bistable switching between metastable states in the presence…

Let $(X,d)$ be a metric space and $f_{1,\infty}=\{f_n\}_{i=0}^{\infty}$ be a sequence of continuous maps $f_n:X\rightarrow X$ such that $(f_n)$ converges uniformly to a continuous map $f$. We investigate which conditions ensure that the…

In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…

In this paper, we consider the family of planar piecewise linear differential systems with two zones separated by a straight line without sliding regions, that is, differential systems whose flow transversally crosses the switching line…

We study a class of discontinuous vector fields brought to our attention by multi-legged animal locomotion. Such vector fields arise not only in biomechanics, but also in robotics, neuroscience, and electrical engineering, to name a few…

We investigate the rotation sets of open billiards in $\mathbb{R}^N$ for the natural observable related to a starting point of a given billiard trajectory. We prove that the general rotation set is convex and the set of all convex…

We consider a class of discontinuous piecewise linear differential systems in $\mathbb{R}^3$ with two pieces separated by a plane. In this class we show that there exist differential systems having: a unique limit cycle, a unique…

In the present study we consider planar piecewise linear vector fields with two zones separated by the straight line $x=0$. Our goal is to study the existence of simultaneous crossing and sliding limit cycles for such a class of vector…

The aim of this paper is to explore the possibilities of Conley index techniques in the study of heteroclinic connections between finite and infinite invariant sets. For this, we remind the reader of the Poincar\'e compactification: this…

The percolation threshold for flow or conduction through voids surrounding randomly placed spheres is rigorously calculated. With large scale Monte Carlo simulations, we give a rigorous continuum treatment to the geometry of the…

In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dynamics of the populations of predators and their prey in a…

We study discrete-time dynamical systems that switch between different evolution rules based on thresholds that themselves adapt over time. Specifically, we analyze the coupled recursion $a_{n+1} = f(a_n)$ if $a_n \leq c_n$ and $a_{n+1} =…

This paper studies a basic model of a dynamical distribution network, where the network topology is given by a directed graph with storage variables corresponding to the vertices and flow inputs corresponding to the edges. We aim at…

We analyze the dynamics of a class of $\mathbb{Z}_{2n}$-equivariant differential equations on the plane, depending on 4 real parameters. This study is the generalisation to $\mathbb{Z}_{2n}$ of previous works with $\mathbb{Z}_4$ and…

This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and…

We consider the 1-parameter family of planar quintic systems, $\dot x= y^3-x^3$, $\dot y= -x+my^5$, introduced by A. Bacciotti in 1985. It is known that it has at most one limit cycle and that it can exist only when the parameter $m$ is in…

In this paper, we apply the averaging method via Brouwer degree in a class of planar systems given by a linear center perturbed by a sum of continuous homogeneous vector fields, to study lower bounds for their number of limit cycles. Our…

Consider a navigation rule defined on a graph that maps every vertex of the graph to a vertex in such a way that the navigation rule commutes with every automorphism of the graph. It is to say that the navigation rule applied to the…