Related papers: Topologically-based fractional diffusion and emerg…
We investigate in detail a recent model of colliding mobile agents [Phys. Rev. Lett.~96, 088702], used as an alternative approach to construct evolving networks of interactions formed by the collisions governed by suitable dynamical rules.…
Particle- and agent-based systems are a ubiquitous modeling tool in many disciplines. We consider the fundamental problem of inferring interaction kernels from observations of agent-based dynamical systems given observations of…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Recent foundational studies have established the bulk-edge correspondence for nonlinear eigenvalue problems using auxiliary eigenvalues $\hat{H}\Psi=\omega S(\omega)\Psi$, spanning both linear [T. Isobe et al., Phys. Rev. Lett. 132, 126601…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…
We propose a class of nonlocal diffusion systems on time-varying domains, and fully characterize their asymptotic dynamics in the asymptotically fixed, time-periodic and unbounded cases. The kernel is not necessarily symmetric or compactly…
The emergence of a spatially-organized population distribution depends on the dynamics of the population and mediators of interaction (activators and inhibitors). Two broad classes of models have been used to investigate when and how…
Animal swarms displaying a variety of typical flocking patterns would not exist without underlying safe, optimal and stable dynamics of the individuals. The emergence of these universal patterns can be efficiently reconstructed with…
We elucidate that the diffusive systems, which are widely found in nature, can be a new platform of the bulk-edge correspondence, a representative topological phenomenon. Using a discretized diffusion equation, we demonstrate the emergence…
We consider the collective behaviour of active particles that locally align with their neighbours. Agent-based simulation models have previously shown that in one dimension, these particles can form into a flock that maintains its stability…
An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the one-dimensional torus, arising in population dynamics, is proposed and analyzed. The kernels are assumed to be in detailed balance and satisfy a weak…
Understanding how simple local interactions give rise to emergent exploration patterns is a fundamental question in statistical physics. We introduce a minimal model of two coupled agents that avoid retracing their own paths while being…
The paper introduces a novel topological method for prediction and modeling for a nonlinear time--series that exhibit recurring patterns. According to the model, global manifold of the reconstructed state--space can be approximated by a few…
Consider the following asynchronous, opportunistic communication model over a graph $G$: in each round, one edge is activated uniformly and independently at random and (only) its two endpoints can exchange messages and perform local…
We consider the compressible Euler system with a family of nonlinear velocity alignments. The system is a nonlinear extension of the Euler-alignment system in collective dynamics. We show the asymptotic emergent phenomena of the system:…
In this paper, we present a model describing the collective motion of birds. The model introduces spontaneous changes in direction which are initialized by few agents, here referred as leaders, whose influence act on their nearest…
Many biological systems collectively construct complex, adaptive, and functional architectures, where function emerges from bottom-up building processes rather than top-down planning or centralized control. However, general strategies for…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
Climate change is reshaping species interactions and movement across fragmented landscapes. Despite this, most mathematical models assume random diffusion, overlooking the influence of directed movement. Here, we develop a graph based…
Diffusion-based generative models employ stochastic differential equations (SDEs) and their equivalent probability flow ordinary differential equations (ODEs) to establish a smooth transformation between complex high-dimensional data…