Related papers: Fine structure of one-dimensional discrete point s…
Relationship for dynamical properties in the vicinity of fixed points between two-dimensional continuous and its positivity-preserving discretized dynamical systems is studied. Based on linear stability analysis, we reveal the conditions…
This work is a comparative study between the existence of fixed point for homomorphisms in a class of binary relationnal systems and the existence of fixed point for nonexpansive mappings in semimetric spaces.
In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…
This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary…
This paper is devoted to discrete mechanical systems subject to external forces. We introduce a discrete version of systems with Rayleigh-type forces, obtain the equations of motion and characterize the equivalence for these systems.…
We show how a fine, multiple-peak structure can arise in the off-resonance, zero-bias conductance of Coulomb blockade systems. In order to understand how this effect comes about one must abandon the orthodox, mean-field understanding of the…
A dynamic system, which is used in the neural network theory, Ising spin glasses and factor analysis, has been investigated. The properties of the connection matrix, which guarantee the coincidence of the set of the fixed points of the…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…
We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
This note aims at obtaining a variational characterization of complex structures by means of a calculus of variations for real vector bundle valued differential forms, and outlines a perspective to study existence questions via functionals…
We study local features, and provide a topological insight into the global structure of the probability density distribution and of the pattern of the optimal paths for large rare fluctuations away from a stable state. In contrast to…
We study discrete fixed point sets of holomorphic self-maps of complex manifolds. The main attention is focused on the cardinality of this set and its configuration. As a consequence of one of our observations, a bounded domain in ${\Bbb…
Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…
We prove fixed point theorems in a space with a distance function that takes values in a partially ordered monoid. On the one hand, such an approach allows one to generalize some fixed point theorems in a broad class of spaces, including…
Boundary driven diffusive systems describe a broad range of transport phenomena. We study large deviations of the density profile in these systems, using numerical and analytical methods. We find that the large deviation may be…
We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…
We study the behaviour of discrete dynamical systems generated by a continuous map $f$ of a compact real interval into itself where at randomly chosen times a function different from $f$ - so called impulse function is applied. We show that…