Keeping speed and distance for aligned motion

Abstract

The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space and time we find that if two particles arrive symmetrically in a plane at a large angle, then (i) radial repulsion and (ii) linear self-propelling toward a fixed preferred speed are sufficient for them to depart at a smaller angle. For this local gain of momentum explicit velocity alignment is not necessary, nor are adhesion or attraction, inelasticity or anisotropy of the particles, or nonlinear drag. With many particles obeying these microscopic rules of motion we find that their spatial confinement to a square with periodic boundaries (which is an indirect form of attraction) leads to stable macroscopic ordering. As a function of the strength of added noise we see--at finite system sizes--a critical slowing down close to the order-disorder boundary and a discontinuous transition. After varying the density of particles at constant system size and varying the size of the system with constant particle density we predict that in the infinite system size (or density) limit the hysteresis loop disappears and the transition becomes continuous. We note that animals, humans, drones, etc., tend to move asynchronously and are often more responsive to motion than positions. Thus, for them velocity-based continuous models can provide higher precision than coordinate-based models. An additional characteristic and realistic feature of the model is that convergence to the ordered state is fastest at a finite density, which is in contrast to models applying (discontinuous) explicit velocity alignments and discretized time. To summarize, we find that the investigated model can provide a minimal description of flocking.

Spatial flocking: Control by speed, distance, noise and delay

“…With the parameters selected in Sec we find that the noise level ξ = 50 can already keep an initially disordered system from reaching order, however, it is not sufficient to destroy order in an initially ordered system. We conclude that the system shows hysteresis, which is similar to the 2-dimensional version of the model [ 32 ]. Finally, note that this behavior stabilizes the ordered state, and at the same time makes transitions fast.…”

“…Here we investigate the 3-dimensional version of the generic model that was suggested in [ 31 ] and analyzed for 2 dimensions in [ 32 ]. The model is continuous in both space and time, and it contains N agents.…”

ACSEE: Antagonistic Crowd Simulation Model With Emotional Contagion and Evolutionary Game Theory

“…Emotion is a psychological parameter and has a significant influence on individuals in a crowd [5], [25], [26], [27]. Emotional contagion is closely related to human movement [28], [29], [30]. In this subsection, we introduce some representative works about emotional contagion [4].…”

Empirical analysis of complex social and financial networks

“…Using concepts from statistical physics and applying the approach of mathematical modeling developed on physical systems to a wider range of complex phenomena has lead to important results in various fields; some of these are closer to traditional research foci in physics, while others are more apart. Examples include statistical models of various biological phenomena, including flocking and herding behavior [197,146,73,198,92], mathematical models for ecology, evolution and the emergence of cooperation [139,201,178,185]; modeling pattern formation in various systems [85,52,122] and the application of the concept of fractality in both the geometric and dynamic sense [133,15,87]; chaos theory [59] to gain a better understanding of systems with a very high dimensionality [13]; models of the economy and various social phenomena [134,45,173,196,104,84]; and the study of networks, which themselves can be used to describe a wide range of complex systems around us [149,29,66,30,97,142]. Many of these approaches make use of the concepts of statistical physics, aiming to compute relevant macroscopic parameters of a system made up of many interacting parts.…”