Related papers: Flocking and non-flocking behavior in a stochastic…
Understanding collective self-organization in active matter, such as bird flocks and fish schools, remains a grand challenge in physics. Interactions that induce alignment are essential for flocking; however, alignment alone is generally…
Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by…
Collective behaviors such as swarming and flocking emerge from simple, decentralized interactions in biological systems. Existing models, such as Vicsek and Cucker-Smale, lack collision avoidance, whereas the Olfati-Saber model imposes…
The hydrodynamic limit of a kinetic Cucker-Smale model is investigated. In addition to the free-transport of individuals and the Cucker-Smale alignment operator, the model under consideration includes a strong local alignment term. This…
Flocking is a coordinated collective behavior that results from local sensing between individual agents that have a tendency to orient towards each other. Flocking is common among animal groups and might also be useful in robotic swarms. In…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Recent experimental evidence suggests that interactions in flocks of birds do not involve a characteristic length scale. Bird flocks have also been revealed to have an inhomogeneous density distribution, with the density of birds near the…
This paper presents an elementary proof of quantitative uniform-in-time propagation of chaos for the Cucker--Smale model under sufficiently strong interaction. The idea is to combine existing finite-time propagation of chaos estimates with…
The dynamics of well-mixed biological populations is usually studied by mean-field methods and weak-noise expansions. Similar methods have been applied also in spatially extended problems, relying on the fact that these populations are…
We present a 2D lattice model of self-propelled spins that can only change direction upon collision with another spin. We show that even with ballistic motion and minimal cooperativity, these spins display robust flocking behavior at nearly…
The paper introduces a model of collective behavior where agents receive information only from sufficiently dense crowds in their immediate vicinity. The system is an asymmetric, density-induced version of the Cucker-Smale model with…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
We study emergent behaviors of Cucker-Smale(CS) flocks on the hyperboloid $\mathbb{H}^d$ in any dimensions. In a recent work \cite{H-H-K-K-M}, a first-order aggregation model on the hyperboloid was proposed and its emergent dynamics was…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
We present long Monte Carlo simulations of a simple model of biological macroevolution in which births, deaths, and mutational changes in the genome take place at the level of individual organisms. The model displays punctuated equilibria…
For networked systems, Persistent Excitation and Integral Scrambling Condition are conditions ensuring that communication failures between agents can occur, but a minimal level of service is ensured. We consider cooperative multi-agent…
Recent theoretical studies have shown that demographic stochasticity can greatly increase the tendency of asexually reproducing phenotypically diverse organisms to spontaneously evolve into localised clusters, suggesting a simple mechanism…
Phase-transitionlike behavior is found to occur in globally coupled systems of finite number of elements, and its theoretical explanation is provided. The system studied is a population of globally pulse-coupled integrate-and-fire cells…
We consider the effect of introducing a small number of non-aligning agents in a well-formed flock. To this end, we modify a minimal model of active Brownian particles with purely repulsive (excluded volume) forces to introduce an alignment…