Related papers: Serial interconnections of 1-contracting and 2-con…

Certain reductions of the rank 2, genera 2 and 3 Hitchin systems are considered, which are shown to give an integrable system of 2, resp. 3, interacting points on the line. It is shown that the reduced systems are particular cases of a…

We derive analytically the spatial correlation functions for gap fluctuations in two-band scenario with intra- and interband pair-transfer interactions. These functions demonstrate the changes in spatial functionality due to the presence of…

We revisit the problem of existence of stable systems of contracts with arbitrary sets of contracts. We show that stable sets of contracts exists if choices of agents satisfy path-independence. We call such choice functions Plott functions.…

Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts…

Networks are frequently studied algebraically through matrices. In this work, we show that networks may be studied in a more abstract level using results from the theory of matroids by establishing connections to networks by decomposition…

This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…

$k$-level correlation is a local statistic of sequences modulo 1, describing the local spacings of $k$-tuples of elements. For $k = 2$ this is also known as pair correlation. We show that there exists a well spaced increasing sequence of…

We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…

When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appeared permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to…

Heteroclinic connections are trajectories that link invariant sets for an autonomous dynamical flow: these connections can robustly form networks between equilibria, for systems with flow-invariant spaces. In this paper we examine the…

Bermond and Thomassen conjectured that every digraph with minimum outdegree at least $2k-1$ contains $k$ vertex disjoint cycles. So far the conjecture was verified for $k\le 3$. Here we generalise the question asking for all outdegree…

The most general form of a marginal extended perturbation in a two-dimensional system is deduced from scaling considerations. It includes as particular cases extended perturbations decaying either from a surface, a line or a point for which…

We construct a ring of flows where we can decompose autonomous nonlinear dynamical systems into smaller parts, then solve each part and finally put everything together to obtain the exact solution of these systems.

The dynamics by iteration of a function on a compact metric space, sometimes called a cascade, can be extended to the dynamics of a closed relation on such a space. Here we apply this relation dynamics to study semiflows (and their relation…

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the…

High-dimensional/high-fidelity nonlinear dynamical systems appear naturally when the goal is to accurately model real-world phenomena. Many physical properties are thereby encoded in the internal differential structure of these resulting…

Flux binding is a mechanism that is well-understood for global symmetries. Given two systems, each with a global symmetry, gauging the composite symmetry instead of individual symmetries corresponds to the condensation of the composite of…

Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…

Scaffold proteins organize cellular processes by bringing signaling molecules into interaction, sometimes by forming large signalosomes. Several of these scaffolds are known to polymerize. Their assemblies should therefore not be understood…

Compound matrices have found applications in many fields of science including systems and control theory. In particular, a sufficient condition for $k$-contraction is that a logarithmic norm (also called matrix measure) of the $k$-additive…