This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behavior...This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.展开更多
The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key ...The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key features of complex systems, such as dynamic behavior, local interaction, changing neighborhood, etc. This model looks simple, but the nonlinearly coupled relationship makes the theoretical analysis quite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that the neighbor graphs associated with the agents＇ positions satisfy a certain connectivity condition. Much subsequent research effort has been devoted to the analysis of the Vicsek model since the publication of Jadbabaie＇s work. However, an unresolved key problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposed on the model parameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0,2π）, which reveals some fundamental differences between the Vicsek model and its linearized version.展开更多
Because of the low convergence efficiency of the typical Vicsek model,a Vicsek with static summoning points(VSSP)algorithm based on the Vicsek model considering static summoning points is proposed.Firstly,the mathemat...Because of the low convergence efficiency of the typical Vicsek model,a Vicsek with static summoning points(VSSP)algorithm based on the Vicsek model considering static summoning points is proposed.Firstly,the mathematical model of the individual movement total cost on each summoning point is established.Then the individual classification rule is designed according to the initial state of the cluster to obtain the subclusters guided by each summoning point.Finally,the summoning factor is introduced to modify the course angle updating formula of the Vicsek model.To verify the effectiveness of the proposed algorithm and study the effect of the cluster summoning factor on the convergence rate,three groups of simulation experiments under different summoning factors are designed in this paper.To verify the superiority of the VSSP algorithm,the performance of the VSSP algorithm is compared with the classic algorithm by designing the algorithm performance comparison verification experiment.The results show that the algorithm proposed in this paper has good convergence and course angle consistency.The summoning factor is the sensitive factor of cluster convergence.This algorithm can provide a reference for efficient cluster segmentation movement.展开更多
This study extends the self-propelled particle(SPP)model by incorporating a limited vision cone and local density sensing.The results reveal that clusters can simultaneously exhibit velocity polarization and spatial c...This study extends the self-propelled particle(SPP)model by incorporating a limited vision cone and local density sensing.The results reveal that clusters can simultaneously exhibit velocity polarization and spatial cohesion within specific ranges of vision angle and density threshold.The dependence of the dynamical features,including the order parameter and density variation,on the threshold and visual cone is investigated.Furthermore,a critical threshold is identified,which governs the transition between ordered and disordered states and is closely linked to density fluctuations and noise intensity.The clustering results show that the model is explained by the chasing mechanism responsible for cluster formation,density,and shape.These results may stimulate practical applications in swarm maneuvering.展开更多
Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors （e.g., synchronization） of the overal...Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors （e.g., synchronization） of the overall system. In this paper, we will consider a basic class of multi-agent systems that are described by a simplification of the well-known Vicsek model. This model looks simple, but the rigorous theoretical analysis is quite complicated, because there are strong nonlinear interactions among the agents in the model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents＇ trajectories （or on the closed-loop dynamic neighborhood graphs）, which are quite hard to verify in general. In this paper, by introducing a probabilistic framework to this problem, we will provide a complete and rigorous proof for the fact that the overall multi-agent system will synchronize with large probability as long as the number of agents is large enough. The proof is based on a detailed analysis of both the dynamical properties of the nonlinear system evolution and the asymptotic properties of the spectrum of random geometric graphs.展开更多
Over the last ten years, the consensus of multi-agent systems (MAS) has received increasing attention from mechanics, mathematics, physics, engineering sciences, social sciences, and so on. It is well known that the r...Over the last ten years, the consensus of multi-agent systems (MAS) has received increasing attention from mechanics, mathematics, physics, engineering sciences, social sciences, and so on. It is well known that the robustness of consensus of MAS is usually determined by several key factors, including noise, time-delays, and packet drop. In this paper, we introduce a general time-delayed MAS model with noise and also further investigate its robust consensus. In particular, we prove that the proposed algorithm is robust against the bounded time-varying delays and bounded noises. The effectiveness and robustness of the proposed consensus algorithm has been validated in the classical Vicsek model with time-varying delays. And two simulation examples are also given to justify the above theoretical results. These results may have some potential applications in various fields, including mechanics, biology, and engineering sciences.展开更多
The consensus problem of multi-agent systems has attracted wide attention from researchers in recent years, following the initial work of Jadbabaie et al. on the analysis of a simplified Vicsek model. While the origin...The consensus problem of multi-agent systems has attracted wide attention from researchers in recent years, following the initial work of Jadbabaie et al. on the analysis of a simplified Vicsek model. While the original Vicsek model contains noise effects, almost all the existing theoretical results on consensus problem, however, do not take the noise effects into account. The purpose of this paper is to initiate a study of the consensus problems under noise disturbances. First, the class of multi-agent systems under study is transformed into a general time-varying system with noise. Then, for such a system, the equivalent relationships are established among （i） robust consensus, （ii） the positivity of the second smallest eigenvalue of a weighted Laplacian matrix, and （iii） the joint connectivity of the associated dynamical neighbor graphs. Finally, this basic equivalence result is shown to be applicable to several classes of concrete multi-agent models with noise.展开更多
基金the National Natural Science Foundation of China(Grant No.62273033).
文摘This paper presents a comprehensive framework for analyzing phase transitions in collective models such as theVicsek model under various noise types. The Vicsek model, focusing on understanding the collective behaviors of socialanimals, is known due to its discontinuous phase transitions under vector noise. However, its behavior under scalar noiseremains less conclusive. Renowned for its efficacy in the analysis of complex systems under both equilibrium and nonequilibriumstates, the eigen microstate method is employed here for a quantitative examination of the phase transitions inthe Vicsek model under both vector and scalar noises. The study finds that the Vicsek model exhibits discontinuous phasetransitions regardless of noise type. Furthermore, the dichotomy method is utilized to identify the critical points for thesephase transitions. A significant finding is the observed increase in the critical point for discontinuous phase transitions withescalation of population density.
基金the National Natural Science Foundation of China (Grant Nos.60221301 and 60334040)
文摘The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key features of complex systems, such as dynamic behavior, local interaction, changing neighborhood, etc. This model looks simple, but the nonlinearly coupled relationship makes the theoretical analysis quite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that the neighbor graphs associated with the agents＇ positions satisfy a certain connectivity condition. Much subsequent research effort has been devoted to the analysis of the Vicsek model since the publication of Jadbabaie＇s work. However, an unresolved key problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposed on the model parameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0,2π）, which reveals some fundamental differences between the Vicsek model and its linearized version.
基金supported by the National Natural Science Foundation of China(51979193)the China Scholarship Council(201506290080)+1 种基金the China Postdoctoral Science Foundation(2019M653652)the Natural Science Basic Research Plan in Shaanxi Province of China(2019JQ-607).
文摘Because of the low convergence efficiency of the typical Vicsek model,a Vicsek with static summoning points(VSSP)algorithm based on the Vicsek model considering static summoning points is proposed.Firstly,the mathematical model of the individual movement total cost on each summoning point is established.Then the individual classification rule is designed according to the initial state of the cluster to obtain the subclusters guided by each summoning point.Finally,the summoning factor is introduced to modify the course angle updating formula of the Vicsek model.To verify the effectiveness of the proposed algorithm and study the effect of the cluster summoning factor on the convergence rate,three groups of simulation experiments under different summoning factors are designed in this paper.To verify the superiority of the VSSP algorithm,the performance of the VSSP algorithm is compared with the classic algorithm by designing the algorithm performance comparison verification experiment.The results show that the algorithm proposed in this paper has good convergence and course angle consistency.The summoning factor is the sensitive factor of cluster convergence.This algorithm can provide a reference for efficient cluster segmentation movement.
基金Project supported by the Postgraduate Research&Practice Innovation Program of Jiangsu Province(Grant No.KYCX240139)funded by the Youth Independent Innovation Fund of PLA Army Engineering University(Grant No.KYJBJKQTZQ23006)。
文摘This study extends the self-propelled particle(SPP)model by incorporating a limited vision cone and local density sensing.The results reveal that clusters can simultaneously exhibit velocity polarization and spatial cohesion within specific ranges of vision angle and density threshold.The dependence of the dynamical features,including the order parameter and density variation,on the threshold and visual cone is investigated.Furthermore,a critical threshold is identified,which governs the transition between ordered and disordered states and is closely linked to density fluctuations and noise intensity.The clustering results show that the model is explained by the chasing mechanism responsible for cluster formation,density,and shape.These results may stimulate practical applications in swarm maneuvering.
基金The research is supported by National Natural Science Foundation of China under the Grants No. 60221301 and No. 60334040.Acknowledgement The authors would like to thank Prof. Feng TIAN and Dr. Mei LU for providing the proof of Lemma 6 in Appendix B. We would also like to thank Ms. Zhixin Liu for valuable discussions.
文摘Multi-agent systems arise from diverse fields in natural and artificial systems, and a basic problem is to understand how locally interacting agents lead to collective behaviors （e.g., synchronization） of the overall system. In this paper, we will consider a basic class of multi-agent systems that are described by a simplification of the well-known Vicsek model. This model looks simple, but the rigorous theoretical analysis is quite complicated, because there are strong nonlinear interactions among the agents in the model. In fact, most of the existing results on synchronization need to impose a certain connectivity condition on the global behaviors of the agents＇ trajectories （or on the closed-loop dynamic neighborhood graphs）, which are quite hard to verify in general. In this paper, by introducing a probabilistic framework to this problem, we will provide a complete and rigorous proof for the fact that the overall multi-agent system will synchronize with large probability as long as the number of agents is large enough. The proof is based on a detailed analysis of both the dynamical properties of the nonlinear system evolution and the asymptotic properties of the spectrum of random geometric graphs.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60821091, 60772158, 11072254, 61025017)the National Basic Research Program of China ("973" Project) (Grant No. 2007CB310805)the ARC Future Fellowships (Grant No. FT0992226)
文摘Over the last ten years, the consensus of multi-agent systems (MAS) has received increasing attention from mechanics, mathematics, physics, engineering sciences, social sciences, and so on. It is well known that the robustness of consensus of MAS is usually determined by several key factors, including noise, time-delays, and packet drop. In this paper, we introduce a general time-delayed MAS model with noise and also further investigate its robust consensus. In particular, we prove that the proposed algorithm is robust against the bounded time-varying delays and bounded noises. The effectiveness and robustness of the proposed consensus algorithm has been validated in the classical Vicsek model with time-varying delays. And two simulation examples are also given to justify the above theoretical results. These results may have some potential applications in various fields, including mechanics, biology, and engineering sciences.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60821091, 60804043, 60574068)the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No. KJCX3-SYW-S01)
文摘The consensus problem of multi-agent systems has attracted wide attention from researchers in recent years, following the initial work of Jadbabaie et al. on the analysis of a simplified Vicsek model. While the original Vicsek model contains noise effects, almost all the existing theoretical results on consensus problem, however, do not take the noise effects into account. The purpose of this paper is to initiate a study of the consensus problems under noise disturbances. First, the class of multi-agent systems under study is transformed into a general time-varying system with noise. Then, for such a system, the equivalent relationships are established among （i） robust consensus, （ii） the positivity of the second smallest eigenvalue of a weighted Laplacian matrix, and （iii） the joint connectivity of the associated dynamical neighbor graphs. Finally, this basic equivalence result is shown to be applicable to several classes of concrete multi-agent models with noise.
