相关论文: The Heider balance - a continuous approach

A standard result by Smale states that n dimensional strongly cooperative dynamical systems can have arbitrary dynamics when restricted to unordered invariant hyperspaces. In this paper this result is extended to the case when all solutions…

We consider Noether symmetries of the equations defined by the sections of characteristic line bundles of nondegenerate 1-forms and of the associated perturbed systems. It appears that this framework can be used for time-dependent systems…

Degree heterogeneity and latent geometry, also referred to as popularity and similarity, are key explanatory components underlying the structure of real-world networks. The relationship between these components and the statistical…

Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…

In this paper, we prove tight sufficient conditions for traceability and Hamiltonicity of connected graphs with given minimum degree, in terms of Wiener index and Harary index. We also prove some result on Hamiltonicity of balanced…

For integers $k\geq 1$ and $n\geq 2k+1$, the Schrijver graph $S(n,k)$ has as vertices all $k$-element subsets of $[n]:=\{1,2,\ldots,n\}$ that contain no two cyclically adjacent elements, and an edge between any two disjoint sets. More…

In many real-world networks, relationships often go beyond simple dyadic presence or absence; they can be positive, like friendship, alliance, and mutualism, or negative, characterized by enmity, disputes, and competition. To understand the…

We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…

Hybrid dynamical systems with nonlinear dynamics are one of the most general modeling tools for representing robotic systems, especially contact-rich systems. However, providing guarantees regarding the safety or performance of nonlinear…

We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph model in which random instances of a fixed motif are added independently. The binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by adding…

Let $H$ be a complete $r$-uniform hypergraph such that two vertices are marked in each edge as its `boundary' vertices. A linear ordering of the vertex set of $H$ is called an {\em agreeing linear order}, provided all vertices of each edge…

The Einstein relation, relating the steady state fluctuation properties to the linear response to a perturbation, is considered for steady states of stochastic models with a finite state space. We show how an Einstein relation always holds…

An important measure of signed graphs is the line index of balance which has several applications in many fields. However, this graph-theoretic measure was underused for decades because of the inherent complexity in its computation which is…

This paper studies the signed networks in the presence of stubborn links, based on the structural balance theory. Each agent in the network has a mixture of positive and negative links represent friendly and antagonistic interactions and…

Hypergraphs naturally represent higher-order interactions, which persistently appear from social interactions to neural networks and other natural systems. Although their importance is well recognized, a theoretical framework to describe…

Time-delay chaotic systems refer to the hyperchaotic systems with multiple positive Lyapunov exponents. It is characterized by more complex dynamics and a wider range of applications as compared to those non-time-delay chaotic systems. In a…

Bridging equilibrium and nonequilibrium statistical physics attracts sustained interest. Hallmarks of nonequilibrium systems include a breakdown of detailed balance, and an absence of a priori potential function corresponding to the…

We analyze the convergence of the harmonic balance method for computing isolated periodic solutions of a large class of continuously differentiable Hilbert space valued differential-algebraic equations (DAEs). We establish asymptotic…

Polarization, understood as a division into mutually hostile groups, is a common feature of social systems. It is studied in Structural Balance Theory (SBT) in terms of semicycles in signed networks. However, enumerating semicycles is…

Since their inception about a decade ago, dynamic networks which adapt to the state of the nodes have attracted much attention. One simple case of such an adaptive dynamics is a model of social networks in which individuals are typically…