Related papers: Dynamical Models of Dyadic Interactions with Delay

We consider a broad class of stochastic imitation dynamics over networks, encompassing several well known learning models such as the replicator dynamics. In the considered models, players have no global information about the game…

Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way…

We propose a novel class of network models for temporal dyadic interaction data. Our goal is to capture a number of important features often observed in social interactions: sparsity, degree heterogeneity, community structure and…

Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve…

A mathematical model for behavioral changes by pair interactions (i.e. due to direct contact) of individuals is developed. Three kinds of pair interactions can be distinguished: Imitative processes, avoidance processes, and compromising…

Game-theoretical models where the rules of the game and the interaction structure both coevolves with the game dynamics -- multiadaptive games -- capture very flexible situations where cooperation among selfish agents can emerge. In this…

We investigate the effect of a four-dimensional Fourier transform on the formulation of the Navier-Stokes equation in Fourier space and the way the energy is transferred between Fourier components. Since time in a sampled high intensity…

Opinion dynamics of random-walking agents on finite two-dimensional lattices is studied. In the model, the opinion is continuous, and both the lattice and the opinion can be either periodic or non-periodic. At each time step, all agents…

Interactions in active matter systems inherently involve delays due to information processing and actuation lags. We numerically investigate the impact of such delays on the phase behavior of the Vicsek model for motile active matter at a…

This paper examines equilibria in dynamic two-sided matching games, extending Gale and Shapley's foundational model to a non-cooperative, decentralized, and dynamic framework. We focus on markets where agents have utility functions and…

Proposed to study the dynamics of physiological systems in which the evolution depends on the state in a previous time, the Mackey-Glass model exhibits a rich variety of behaviors including periodic or chaotic solutions in vast regions of…

Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…

We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…

The relative dynamics in collision avoidance between individual pedestrians and dyads has been recently studied, and it was shown that individuals may intrude dyads that are not socially interacting. Building on this, our current study…

We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…

Queueing theory has been recently proposed as a framework to model the heavy tailed statistics of human activity patterns. The main predictions are the existence of a power-law distribution for the interevent time of human actions and two…

Relational event data, which consist of events involving pairs of actors over time, are now commonly available at the finest of temporal resolutions. Existing continuous-time methods for modeling such data are based on point processes and…

Varying environmental conditions affect relations between interacting individuals in social dilemmas, thus affecting also the evolution of cooperation. Oftentimes these environmental variations are seasonal and can therefore be…

We study long-range interacting systems perturbed by external stochastic forces. Unlike the case of short-range systems, where stochastic forces usually act locally on each particle, here we consider perturbations by external stochastic…