Swarming transitions in hierarchical societies

Xue, Tingting; Li, Xu; Grassberger, Peter; Chen, Li

doi:10.1103/physrevresearch.2.042017

Cited by 14 publications

(22 citation statements)

References 30 publications

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“…Alongside the previous concerns, here we aim to clarify the nature of all PTs in the Vicsek model. By adopting the structural order parameter [18] and the technique of PDF segmentation [16], we confirm that all PTs between the two neighboring phase are first-order given the system is large enough. The existing problem is that the structural order parameter is still insensitive to the parameter change in some regions that makes the PDF segmentation bad and thus less precise in characterizing the PTs.…”

Section: Discussionmentioning

confidence: 67%

“…In fact, there are three rather than simply two phases (ordered and disordered), i.e. the disordered gas-like state, the ordered liquid-like state, and the coexistence of ordered bands and disordered gas due to the density-velocity feedback [15,16]. More recently, with Eigen microstates approach, reference [17] revealed that the PT in the Vicsek model is essentially a hybrid of continuous and discontinuous PTs, but the discontinuous component dominates as the system size goes infinity.…”

Section: Introductionmentioning

confidence: 99%

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Machine learning phases in swarming systems

Xue

Chen

et al. 2023

Mach. Learn.: Sci. Technol.

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Recent years have witnessed a growing interest in using machine learning to predict and identify phase transitions in various systems. Here we adopt convolutional neural networks (CNNs) to study the phase transitions of Vicsek model, solving the problem that traditional order parameters are insufficiently able to do. Within the large-scale simulations, there are four phases, and we confirm that all the phase transitions between two neighboring phases are first-order. We have successfully classified the phase by using CNNs with a high accuracy and identified the phase transition points, while traditional approaches using various order parameters fail to obtain. These results indicate the great potential of machine learning approach in understanding the complexities in collective behaviors, and in related complex systems in general.

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Section: Discussionmentioning

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Machine learning phases in swarming systems

Xue

Chen

et al. 2023

Mach. Learn.: Sci. Technol.

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“…This function enables us to distinguish first and second order phase transitions, such that it is continuous in second order transitions, while it shows a very sharp discontinuity for first order phase transitions, see for example [26]. We see this function for two β values in Fig.…”

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confidence: 85%

“…This reveals that the system exhibits a discontinuity at the point where the second peak is born (λ [13,14,22]. As a standard approach for bimodal PDFs [26], we divide the data at the valley point between s * 1 and s * 2 (with PDFs represented by P 1 (s * ) and P 2 (s * ) respectively), and average to find two s * i , i = 1, 2 for two branches (this enables us find the structure of the transition, otherwise a structure like β = 0 case is obtained, see Fig. 3 in the SM).…”

mentioning

confidence: 99%

Stochastic and deterministic dynamics in networks with excitable nodes

Rahimi-Majd¹,

Restrepo²,

Nattagh-Najafi³

2021

Preprint

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The analysis of the dynamics of a large class of excitable systems on locally tree-like networks leads to the conclusion that at λ = 1 a continuous phase transition takes place, where λ is the largest eigenvalue of the adjacency matrix of the network. This paper is devoted to evaluate this claim for a more general case where the assumption of the linearity of the dynamical transfer function is violated with a non-linearity parameter β which interpolates between stochastic (β = 0) and deterministic (β → ∞) dynamics. Our model shows a rich phase diagram with an absorbing state and extended critical and oscillatory regimes separated by transition and bifurcation lines which depend on the initial state. We test initial states with (I) only one initial excited node, (II) a fixed fraction (10%) of excited nodes, for all of which the transition is of first order for β > 0 with a hysteresis effect and a gap function. For the case (I) in the thermodynamic limit the absorbing state in the only phase for all λ values and β > 0. We further develop mean-field theories for cases (I) and (II). For case (II) we obtain an analytic one-dimensional map which explains the essential properties of the model, including the hysteresis diagrams and fixed points of the dynamics.

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“…However, a consensus is that our society is more often composed by heterogeneous individuals where they differ in many aspects such as their occupations, social statuses, cultural backgrounds etc [24] that potentially affect their decision-makings. The statement is also true in nature, like the reported examples homing pigeons [25] and white storks [26], where a small fraction of the group take the lead of decision-making regarding their movement direction and the soical hierachy potentially affects their swarming transitions [27]. Recently, researchers start to consider the impact of non-identical individuality and find that the population heterogeneity generally leads to better cooperation outcomes [28][29][30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Social hierarchy promotes the cooperation prevalence

Liang,

Zhang,

Zheng

et al. 2020

Preprint

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Social hierarchy is important that can not be ignored in human socioeconomic activities and in the animal world. Here we incorporate this factor into the evolutionary game to see what impact it could have on the cooperation outcome. The probabilistic strategy adoption between two players is then not only determined by their payoffs, but also by their hierarchy difference -players in the high rank are more likely to reproduce their strategies than the peers in the low rank. Through simulating the evolution of Prisoners' dilemma game with three different hierarchical distributions: uniform, exponential and power-law, we find that the levels of cooperation are enhanced in all cases, and the enhancement is optimal in the uniform case. The enhancement is due to the fact that the presence of hierarchy facilitates the formation of cooperation clusters with highrank players acting as the nucleation cores. We also study a two-hierarchy model, where similar cooperation promotion is revealed and some theoretical analysis are provided. Our finding implies that social hierarchy may be not that harmful to cooperation than previously thought.

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Swarming transitions in hierarchical societies

Cited by 14 publications

References 30 publications

Machine learning phases in swarming systems

Machine learning phases in swarming systems

Stochastic and deterministic dynamics in networks with excitable nodes

Social hierarchy promotes the cooperation prevalence

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