Cucker-Smale Flocking With Inter-Particle Bonding Forces

Abstract

2617queue lengths q1(t2N ), q2(t2N ) are equal to the optimal cyclic solutions and the condition (36) has to be satisfied. VI. CONCLUSIONFor the simplified isolated controlled intersection, in the case when the criterion J is a strictly increasing linear function of the queue lengths, we can compute the optimal switching sequence for the steady-state problem with constant cycle length by solving a LP problem analytically. A necessary and sufficient condition for the steady-state control with constant cycle length was also derived. The N-stages control problem was formulated. It is shown that the N-stages control problem can be solved by LP if the criterion J is linear and strictly increasing. Furthermore, N-stages control can be used to bring the queue lengths to optimum. REFERENCES[1] T.-H. Chang and J.-T. Lin, "Optimal signal timing for an oversaturated intersection," Transport. Res. B, vol. 34, no. 6, pp. 471-491, 2000. [2] B. De Schutter, "Optimizing acyclic traffic signal switching sequences through an extended linear complementarity problem formulation," Eur.Abstract-The Cucker-Smale (CS) flocking model is an interacting particle system, in which each particle updates its velocity by adding to it a weighted average of the differences of its velocity with those of other particles. It has been shown that by using the C-S model, the velocities of particles converge to a common value despite the absence of a central command. In this note, we make an extension of the C-S model by introducing additional interaction terms between agents which we refer to as the inter-particle bonding force, in order to incorporate collision avoidance between agents, and at the same time achieve tighter spatial configurations. The proposed inter-particle bonding force makes use of position and velocity information of other agents in order to achieve such separation and cohesion. With the inter-particle bonding forces and the velocity-alignment term of the original C-S model, we show the emergent behavior of asymptotic flocking to spatial equilibrium configurations.

Complete classification of the asymptotical behavior for singular C-S model on the real line

“…In fact, a lot of analysis has been done to explain the emergence of collective behavior in the dynamics of the C-S model. To name a few, avoidance of collision [1,13], flocking in random environment [2,14,24], mean-field limit in deterministic and stochastic sense [4,5], various type of collective behaviors emergence [3,8,9,10,15,16,17,18,20,21,25,27,28,42], local flocking [11,12,23], bonding force [37], generalized flocking [33], singular and hyperbolic limits [41], kinetic equation [19], application to flight formation [38] and flocking with leaders [32], etc. Instead of the original regular communication setting, In the present paper, we will consider the C-S model with singular communication weight ,i.e.…”

How Do Cultural Classes Emerge from Assimilation and Distinction? An Extension of the Cucker-Smale Flocking Model

“…The Cucker-Smale model is recently proposed and has been widely adopted by various disciplines (e.g., Park, Kim, & Ha, 2010;Perea, Elosegui, & Gò mez, 2009) but not yet introduced to sociology, despite of its rich social implications (see Flache & Macy 2011b, as a notable exception). In principle, the model is a simple but dynamic characterization of interactions and mutual influences among social actors.…”

Emergence of mono-cluster flocking in the thermomechanical Cucker–Smale model under switching topologies

“…In 2007, Cucker and Smale [14] introduced a simple second-order Netwon-like model in the spirit of Vicsek's model [44] as an analytically manageable model, and they derived sufficient frameworks leading to the global and local asymptotic flocking on the complete graph. After their work, the Cucker-Smale(CS) model has been extensively studied in applied math community from several aspects, e.g., stochastic noises [1,4,13,27], discrete approximation [17,23], random failures [19,20,30,41], time-delayed communications [8,9,21,34], collision avoidance [10], network topologies [11,12,18,32,33,39,42], mean-field limit [26,28], kinetic and hydrodynamic descriptions [5,6,22,29,40], nonsymmetric communication networks [36], bonding force [38], extra internal variables [24,25], etc (see recent survey articles [2,7]).…”