Related papers: The boundary of chaos for interval mappings
A temporal graph can be represented by a graph with an edge labelling, such that an edge is present in the network if and only if the edge is assigned the corresponding time label. A journey is a labelled path in a temporal graph such that…
Many complex systems can be modeled by temporal networks, whose organization often evolves through distinct structural phases. Detecting the change points that delimit these phases is both important and challenging. In this work, we extend…
We investigate the properties of chain recurrent, chain transitive, and chain mixing maps (generalizations of the well-known notions of non-wandering, topologically transitive, and topologically mixing maps). We describe the structure of…
This continues the investigation of a combinatorial model for the variation of dynamics in the family of rational maps of degree two, by concentrating on those varieties in which one critical point is periodic. We prove some general results…
We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…
The generalization properties of an attractive network of non monotonic neurons which infers concepts from samples are studied. The macroscopic dynamics for the overlap between the state of the neurons with the concepts, well as the…
Given a dynamical system, we study the so-called space of shift functions thus introducing another vision on bifurcations and chaos. As an application of the obtained results, we give a partial solution to an open problem formulated in…
The set of points that escape to infinity under iteration of a cosine map, that is, of the form $C_{a,b} \colon z \mapsto ae^z+be^{-z}$ for $a,b\in \mathbb{C}^\ast$, consists of a collection of injective curves, called dynamic rays. If a…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
We exhibit a family of dynamical systems arising from rational points on elliptic curves in an attempt to mimic the familiar toral automorphisms. At the non-archimedean primes, a continuous map is constructed on the local elliptic curve…
The term boundary crisis refers to the destruction or creation of a chaotic attractor when parameters vary. The locus of a boundary crisis may contain regions of positive Lebesgue measure marking the transition from regular dynamics to the…
We study a class of chainable continua which contains, among others, all inverse limit spaces generated by a single interval bonding map which is piecewise monotone and locally eventually onto. Such spaces are realized as attractors of…
We introduce an information-theoretic framework for smooth structures on topological manifolds, replacing coordinate charts with small-scale entropy data of local probability probes. A concise set of axioms identifies admissible coordinate…
We consider generic families $X_\param$ of smooth dynamical systems depending on parameters $\param\in P$ where $P$ is a 2-dimensional simply connected domain and assume that each $X_\param$ only has a finite number of restpoints and…
We study the asymptotic behavior of the number of paths of length $N$ on several classes of infinite graphs with a single special vertex. This vertex can work as an entropic trap for the path, i.e. under certain conditions the dominant part…
The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic…
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…
The Lindblad equation describes the dissipative time evolution of a density matrix that characterizes an open quantum system in contact with its environment. The widespread ensemble interpretation of a density matrix requires its time…
Topological entropy is a measure of complex dynamics. In this regard, multimodal maps play an important role when it comes to study low-dimensional chaotic dynamics or explain some features of higher dimensional complex dynamics with…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…