Related papers: Phase Space Structures of k-threshold Sequential D…

In this paper we continue our studies of the phase space geometry and dynamics associated with index k saddles (k > 1) of the potential energy surface. Using normal form theory, we give an explicit formula for a "dividing surface" in phase…

We analyst in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems (see Phys. Rev. Lett . vol. 113, 264102 (2014)) by application to the Tangled Nature Model of evolutionary…

Motility-induced phase separation (MIPS) is a paradigmatic non-equilibrium transition in active matter, determined by the P\'eclet number and packing fraction. We investigate the single-phase and phase-separated regimes of MIPS using a…

In this paper, the reachability of dimension-bounded linear systems is investigated.Since state dimensions of dimension-bounded linear systems vary with time, the expression of state dimension at each time is provided.A method for judging…

This article is focused on two related topics within the study of partial differential equations (PDEs) that illustrate a beautiful connection between dynamics, topology, and analysis: stability and spatial dynamics. The first is a property…

We derive a two-dimensional symplectic map for particle motion at the plasma edge by modeling the electrostatic potential as a superposition of integer spatial harmonics with relative phase shift, then reduce it to a two-wave model to study…

Higher Dimensional Automata (HDA) are higher dimensional relatives to transition systems in concurrency theory taking into account to which degree various actions commute. Mathematically, they take the form of labelled cubical complexes. It…

Humans are often incapable of precisely identifying and implementing the desired control strategy in controlling unstable dynamical systems. That is, the operator of a dynamical system treats the current control effort as acceptable even if…

In pattern-forming systems, competition between patterns with different wave numbers can lead to domain structures, which consist of regions with differing wave numbers separated by domain walls. For domain structures well above threshold…

Here we investigate how the positions of a condensed phase can be controlled by using concentration gradients of a regulator that influences phase separation. We consider a mean field model of a ternary mixture where a concentration…

The kinematic dynamo (KD) describes the growth of magnetic fields generated by the flow of a conducting medium in the limit of vanishing backaction of the fields onto the flow. The KD is therefore an important model system for understanding…

Formal analysis of the emergent structural properties of dynamic networks is largely uncharted territory. We focus here on the properties of forward reachable sets (FRS) as a function of the underlying degree distribution and edge duration.…

Most social, technological and biological networks are embedded in a finite dimensional space, and the distance between two nodes influences the likelihood that they link to each other. Indeed, in social systems, the chance that two…

The frequency dependence of dynamical conductivity of the quasi-one-dimensional structures with hydrogen bonds is studied on the basis of pseudospin-electron model. It takes into account the proton-electron interaction, external…

Sociotechnological and geospatial processes exhibit time varying structure that make insight discovery challenging. This paper proposes a new statistical model for such systems, modeled as dynamic networks, to address this challenge. It…

We present a generic threshold model for the co-evolution of the structure of a network and the state of its nodes. We focus on regular directed networks and derive equations for the evolution of the system toward its absorbing state. It is…

We describe a large family of nonequilibrium steady states (NESS) corresponding to forced flows over obstacles. The spatial structure at large distances from the obstacle is shown to be universal, and can be quantitatively characterised in…

Modeling long range dependencies in sequential data is a fundamental step towards attaining human-level performance in many modalities such as text, vision, audio and video. While attention-based models are a popular and effective choice in…

The phase diagram, ($T,\rho$), of a finite, constrained, and classical system is built from the analysis of cluster distributions in phase and configurational space. The obtained phase diagram can be split in three regions. One, low density…

Recently, a framework for analyzing time series by constructing an associated complex network has attracted significant research interest. One of the advantages of the complex network method for studying time series is that complex network…