Related papers: Cucker-Smale Flocking Under Hierarchical Leadershi…
Social hierarchy is important that can not be ignored in human socioeconomic activities and in the animal world. Here we incorporate this factor into the evolutionary game to see what impact it could have on the cooperation outcome. The…
Many organisms live in populations structured by space and by class, exhibit plastic responses to their social partners, and are subject to non-additive ecological and fitness effects. Social evolution theory has long recognized that all of…
We study the (hydro-)dynamics of multi-species driven by alignment. What distinguishes the different species is the protocol of their interaction with the rest of the crowd: the collective motion is described by different communication…
We propose a non-equilibrium continuum dynamical model for the collective motion of large groups of biological organisms (e.g., flocks of birds, slime molds, etc.) Our model becomes highly non-trivial, and different from the equilibrium…
Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…
Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is mainly based on empirical fits to…
We present a new stochastic particle system on networks which describes the flocking behavior and pattern formation. More precisely, we consider Cucker-Smale particles with decentralized formation control and multiplicative noises on…
Social behaviors involving the interaction of multiple individuals are complex and frequently crucial for an animal's survival. These interactions, ranging across sensory modalities, length scales, and time scales, are often subtle and…
We present some recent development in modeling concurrent emergence of collective behaviors, namely, the emergence of clustering, flocking and synchronization at the same time. We derive two new models, namely Swarmalator-Vicsek and…
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…
The ability to capture detailed interactions among individuals in a social group is foundational to our study of animal behavior and neuroscience. Recent advances in deep learning and computer vision are driving rapid progress in methods…
We present a sufficient condition of the complete position flocking theorem for the Cucker-Smale type model on the unit sphere with an inter-particle bonding force. For this second order dynamical system derived in [Choi, S.-H., Kwon, D.…
The ways in which natural selection can allow the proliferation of cooperative behavior have long been seen as a central problem in evolutionary biology. Most of the literature has focused on interactions between pairs of individuals and on…
Mathematical models for systems of interacting agents using simple local rules have been proposed and shown to exhibit emergent swarming behavior. Most of these models are constructed by intuition or manual observations of real phenomena,…
Collective behavior in animals has long been modeled through self-propelled particle models, which reproduce striking group-level phenomena through abstract interaction forces. Yet these models are fundamentally descriptive: they leave open…
Collective motion in animals and cells often exhibits rapid reorientations and scale-free velocity correlations. This allows information to spread rapidly through the group, allowing an adequate collective response to environmental changes…
Local interactions, when individuals meet, can regulate collective behavior. In a system without any central control, the rate of interaction may depend simply on how the individuals move around. But interactions could in turn influence…
Cooperation plays a fundamental role in societal and biological domains, and the population structure profoundly shapes the dynamics of evolution. Practically, individuals behave either altruistically or egoistically in multiple groups,…
The Cucker-Smale flocking model belongs to a wide class of kinetic models that describe a collective motion of interacting particles that exhibit some specific tendency e.g. to aggregate, flock or disperse. The paper examines the kinetic…
The purpose of this paper is to consider flocking formations of a second order dynamic system on a sphere with a Cucker-Smale type flocking operator and cooperative control. The flocking operator consists of a weighted control parameter and…