Research On Pattern Control And Decision-making Mechanism Of Collective Dynamical Systems

There are abundant pattern phases and cooperative behaviors in biological and physical systems in nature,individuals with low intelligence can stimulate complex swarm intelligence through interaction.On the one hand,the research of collective dynamical systems helps to reveal the mechanism behind the complex self-organization behavior of collective motion,and on the other hand,the related theories and technologies derived from it are expected to serve major national strategic needs such as intelligent manufacturing and unmanned swarm system control.This paper mainly combines the concept of spin in complex system,and conducts related research on the pattern phase control and collective decision-making problems of collective dynamical systems,and the following research results are obtained:For two types of collective behaviors,such as microscopic material pattern phase transition and macroscopic starling collective turning,based on Hamilton’s principle,the spin models in the collective dynamical systems are explored.It is revealed that the interaction between individuals can be described by the Hamiltonian function.It is clarified that the spin characterizes the orientation of particles in the physical collective model,and controls the turning of the birds in the biological collective model.Furthermore,some methods such as order parameter analysis and kernel density estimation are introduced to analyze the characteristics of collective motion.For the microscopic physical collective system,a regulating pattern phase method for the collective dynamical systems is proposed.Based on the spin model considering the external field,the evolution equation of the microscopic particle’s spin is solved by Hamiltonian dynamics.By fine-tuning the coupling strength and the external field strength in the spin model,four patterns of "vortex","ferromagnet","worm",and "antiferromagnet" and phase transition between them are observed in spin particles.The critical state of the pattern phase transition of the collective system is quantitatively studied,and the mechanism of the phase transition is revealed.This work provides a new idea for understanding the evolution and internal mechanism of collective dynamical systems.For the macroscopic biological collective system,the collective decision-making mechanism of the collective dynamical systems is studied.A self-propelled particle model considering both spin and collision avoidance mechanism is established.It is revealed that the group direction has a phase transition from the compromising phase(i.e.,following the group average)to the preferred phase(i.e.,aligning to a leader cluster),and the key factors affecting the phase transition are the size of the leader clusters and the divergence between preferred directions.Through the kernel density estimation method,it is found that the damping factor related to the information propagation efficiency helps to attenuate the preference-switching phase transition.The work shows that fast and robust information transfer helps groups maintain cohesion and that democratic collective decision-making often stems from simple interactions.