Research On The Kinetic Modeling Of Intelligent Particle Groups In Complex Domains

For intelligent particle groups moving according to their respective population goals in complex rectangular chunked region,this thesis tries to investigate their macroscopic motion laws by a kinetic modeling approach.To simplify the problem,in this thesis we focus on the simplest,three-chunked geometric region with connected doors on the left and right.The particle groups kinetic model is between microscopic and macroscopic.Firstly,the interaction of microscopic individuals is modeled by using the tools of game theory,and the collective behavior of these particles satisfies the continuity condition of the dynamics equation,under the condition of complex chunking of the region,it is very important to construct a more reasonable interaction vector field between the particles and the region,and this interaction vector field depends on the geometric condition of the region,which is mainly characterized by the geometry of the“doors" and "walls" of the designed region.The velocity function of the particle groups motion and the inter-particle interaction are localized,but they are very different.The velocity function depends on the sum of the local density functions of all particle groups,and the interparticle interaction depends on the local particle density functions of different motion directions.There are two types of inter-particle interactions:"following the motion of other particles of the population" and " moving in the direction of a less dense population of particles".This thesis first analyzes the interaction of the motion of one group,and the motion of multiple groups can be treated similarly,but slightly different.From the thesis we can see that multiple particle groups can define their own unique microscopic interactions according to the different groups,i.e.,the interaction of particle groups with doors,walls and inter-particle interactions can be different according to the different groups,and the microscopic interactions have a certain population property.In this thesis,we define different particle groups interactions with doors and interactions with walls as inconsistent,and restrict the inter-particle following property(following the motion of other particles)to this group,i.e.,particles can only follow the motion of particles in their own group,but define the inter-particle blocking avoidance property(avoiding congestion)as global.This thesis is dedicated to providing a macroscopic model framework of multi-species intelligent particle group dynamics.As for the microscopic interactions with in each particle group can have various definitions.Numerical simulations are mainly used to study the relationship between the particle groups motion time and the initial distribution of the groups and the size of the exit and the group speed.