相关论文: Dynamics of Influence on Hierarchical Structures

The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…

A general approach for the description of spin systems on hierarchial lattices with coordination number $q$ as a dynamical variable is proposed. The ferromagnetic Ising model on the Bethe lattice was studied as a simple example…

In this work we study the Boolean Networks of different geometric shape and lattice organization. It was revealed that no only a spatial shape but also type of lattice are very important for definition of the structure-dynamics relation.…

The dynamical behaviours of a kinetically constrained spin model (Fredrickson-Andersen model) on a Bethe lattice are investigated by a perturbation analysis that provides exact final states above the nonergodic transition point. It is…

In this paper, we mathematically formulate the interaction and dynamics of a hierarchical complex social system where each agent is seen as an array of many variables. The formation of identities and modifications can be studied by using…

Quantum dynamics of strongly correlated systems is a challenging problem. Although the low energy fractional excitations of one dimensional integrable models are often well-understood, exploring quantum dynamics in these systems remains…

We show that facilitated spin mixtures with a tunable facilitation reproduce, on a Bethe lattice, the simplest higher-order singularity scenario predicted by the mode-coupling theory (MCT) of liquid-glass transition. Depending on the…

Bethe lattice spins glasses are supposed to be marginally stable, i.e. their equilibrium probability distribution changes discontinuously when we add an external perturbation. So far the problem of a spin glass on a Bethe lattice has been…

We studied the effects of spatial configuration on collective dynamics in a nearest-neighbour and diffusively coupled lattice of heterogeneous nodes. The networks contained nodes from two populations, which differed in their intrinsic…

In this short note we prove a hierarchical stability result that applies to hybrid dynamical systems satisfying the hybrid basic conditions of (Goebel et al., 2012). In particular, we establish sufficient conditions for uniform asymptotic…

We unveil the mechanism for the formation of puzzled boundary-localized bound states in a spinless fermionic open lattice with nearest-neighbor interactions. By solving the Bethe-ansatz equation analytically, we uncover asymmetrical string…

Driven non-equilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional…

The Hubbard model is known to accommodate various electronic orders, including stripes, which are important for understanding the physics of cuprates. We study spin-stripe order in the square lattice Hubbard model as a function of doping…

We present an exact treatment of the hysteresis behavior of the zero-temperature random-field Ising model on a Bethe lattice when it is driven by an external field and evolved according to a 2-spin-flip dynamics. We focus on lattice…

Considering deterministic classical lattice systems with continuous variables, we show that, if the initial conditions are sampled according to a probability distribution in which the dynamical variables are statistically independent, the…

The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…

In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…

We show that facilitated spin models of cooperative dynamics introduced by Fredrickson and Andersen display on Bethe lattices a glassy behaviour similar to the one predicted by the mode-coupling theory of supercooled liquids and the…

Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…

We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two…