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Register a new userInternal character dictates phase transition dynamics between isolation and cohesive grouping
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We show that accounting for internal character among interacting, heterogeneous entities generates rich phase transition behavior between isolation and cohesive dynamical grouping. Our analytical and numerical calculations reveal different critical points arising for different character-dependent grouping mechanisms. These critical points move in opposite directions as the populations diversity decreases. Our analytical theory helps explain why a particular class of universality is so common in the real world, despite fundamental differences in the underlying entities. Furthermore, it correctly predicts the non-monotonic temporal variation in connectivity observed recently in one such system.
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We introduce a simple model of a growing system with $m$ competing communities. The model corresponds to the phenomenon of defeats suffered by social groups living in isolation. A nonequilibrium phase transition is observed when at critical time $t_c$ the first isolated cluster occurs. In the one-dimensional system the volume of the new phase, i.e. the number of the isolated individuals, increases with time as $Z sim t^3$. For a large number of possible communities the critical density of filled space equals to $rho_c = (m/N)^{1/3}$ where $N$ is the system size. A similar transition is observed for ErdH{o}s-R{e}nyi random graphs and Barab{a}si-Albert scale-free networks. Analytic results are in agreement with numerical simulations.
In real-world systems, phase transitions often materialize abruptly, making it difficult to design appropriate controls that help uncover underlying processes. Some agent-based computational models display transformations similar to phase transitions. For such cases, it is possible to elicit detailed underlying processes that can be subsequently tested for applicability in real-world systems. In a genetic algorithm, we investigate how a modest difference in the concentration of correct and incorrect knowledge leads to radically different outcomes obtained through learning efforts by a group of agents. We show that a difference in concentration of correct and incorrect knowledge triggers virtuous and vicious cycles that impact the emergent outcome. When virtuous cycles are in operation, delaying the onset of equilibrium attains superior outcomes. For the vicious cycles, reaching equilibrium quickly attains superior outcomes. Our approach helps uncover simple mechanisms by which Nature works, jettisoning the yoke of unrealistic assumptions endemic in mathematics-based approaches. Our explanatory model helps direct research to investigate concentrations of inputs that obtains outcomes on the favourable side of phase transitions. For example, by tracking change in concentration of relevant parameters, scientists may look for reasons why cells cease to reproduce fit cells in organs. This can help design rejuvenation of organs. Further, in the world of physics, our model may inform in situations where the dominant Ising model falls short.
Binary decision-making process is ubiquitous in social life and is of vital significance in many real-world issues, ranging from public health to political campaigns. While continuous opinion evolution independent of discrete choice behavior has been extensively studied, few works unveil how the group binary decision-making result is determined by the coupled dynamics of these two processes. To this end, we propose an agent-based model to study the collective behaviors of individual binary decision-making process through competitive opinion dynamics on social networks. Three key factors are considered: bounded confidence that describes the cognitive scope of the population, stubbornness level that characterizes the opinion updating speed, and the opinion strength that represents the asymmetry power or attractiveness of the two choices. We find that bounded confidence plays an important role in determining competing evolution results. As bounded confidence grows, population opinions experience polarization to consensus, leading to the emergence of phase transition from co-existence to winner-takes-all state under binary decisions. Of particular interest, we show how the combined effects of bounded confidence and asymmetry opinion strength may reverse the initial supportive advantage in competitive dynamics. Notably, our model qualitatively reproduces the important dynamical pattern during a brutal competition, namely, cascading collapse, as observed by real data. Finally and intriguingly, we find that individual cognitive heterogeneity can bring about randomness and unpredictability in binary decision-making process, leading to the emergence of indeterministic oscillation. Our results reveal how the diverse behavioral patterns of binary decision-making can be interpreted by the complicated interactions of the proposed elements, which provides important insights toward competitive dynamics
A finite-time singularity accompanied by log-periodic oscillations shaped the war dynamics and development of the International System during the period 1495 - 1945. The identification of this singularity provides us with a perspective to penetrate and decode the dynamics of the International System. Various regularities in the dynamics of the International System can be identified. These regularities are remarkably consistent, and can be attributed to the connectivity and the growth of connectivity of the International System.
We propose a dynamical model in which a network structure evolves in a self-organized critical (SOC) manner and explain a possible origin of the emergence of fractal and small-world networks. Our model combines a network growth and its decay by failures of nodes. The decay mechanism reflects the instability of large functional networks against cascading overload failures. It is demonstrated that the dynamical system surely exhibits SOC characteristics, such as power-law forms of the avalanche size distribution, the cluster size distribution, and the distribution of the time interval between intermittent avalanches. During the network evolution, fractal networks are spontaneously generated when networks experience critical cascades of failures that lead to a percolation transition. In contrast, networks far from criticality have small-world structures. We also observe the crossover behavior from fractal to small-world structure in the network evolution.
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