Related papers: Fixed points and chaotic dynamics for expansive-co…

Physical systems behave according to their underlying dynamical equations which, in turn, can be identified from experimental data. Explaining data requires selecting mathematical models that best capture the data regularities. Identifying…

In this paper we present a novel methodology based on a topological entropy, the so-called persistent entropy, for addressing the comparison between discrete piecewise linear functions. The comparison is certified by the stability theorem…

We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…

Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…

We derive an algorithm to determine recursively the lap number (minimal number of monotone pieces) of the iterates of unimodal maps of an interval with free end-points. The algorithm is obtained by the sign analysis of the itineraries of…

The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been…

We provide the first step toward developing a hierarchical control-estimation framework to actively plan robot trajectories for anomaly detection in confined spaces. The space is represented globally using a directed region graph, where a…

In this paper we consider a one dimensional liner piecewise-smooth discontinuous map. It is well known that stable periodic orbits exist in this type of map for a specific parameter region. It is also known that the corresponding…

We use the concept of Baire Ergodicity and Ergodic Formalism introduced to study topological and statistical attractors for interval maps, even with discontinuities. For that we also analyze the {\em wandering intervals attractors}. As a…

In this paper, under an abstract setting we establish the spreading properties and the existence, non-existence and global attractivity of spatially heterogeneous steady states for a large class of monotone evolution systems without the…

We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…

We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every…

We develop a new concept of non-positive curvature for metric spaces, based on intersection patterns of closed balls. In contrast to the synthetic approaches of Alexandrov and Buesemann, our concept also applies to metric spaces that might…

We investigate the dynamic phase transition from partially or fully arrested state to spatiotemporal chaos in coupled logistic maps on a small-world network. Persistence of local variables in coarse grained sense acts as an excellent order…

The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain…

Commonly, learning-based topological navigation approaches produce a local policy while preserving some loose connectivity of the space through a topological map. Nevertheless, spurious or missing edges in the topological graph often lead…

Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a…

Dynamical systems, whether continuous or discrete, are used by physicists in order to study non-linear phenomena. In the case of discrete dynamical systems, one of the most used is the quadratic map depending on a parameter. However, some…

Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…