Extreme events, a type of collective behavior in complex networked dynamical systems, often can have catastrophic consequences. To develop effective strategies to control extreme events is of fundamental importance and practical interest. Utilizing transportation dynamics on complex networks as a prototypical setting, we find that making the network “mobile” can effectively suppress extreme events. A striking, resonance-like phenomenon is uncovered, where an optimal degree of mobility exists for which the probability of extreme events is minimized. We derive an analytic theory to understand the mechanism of control at a detailed and quantitative level, and validate the theory numerically. Implications of our finding to current areas such as cybersecurity are discussed.

The relation between flux and fluctuation is fundamental to complex physical systems that support and transport flows. A recently obtained law predicts monotonous enhancement of fluctuation as the average flux is increased, which in principle is valid but only for large systems. For realistic complex systems of small sizes, this law breaks down when both the average flux and fluctuation become large. Here we demonstrate the failure of this law in small systems using real data and model complex networked systems, derive analytically a modified flux-fluctuation law, and validate it through computations of a large number of complex networked systems. Our law is more general in that its predictions agree with numerics and it reduces naturally to the previous law in the limit of large system size, leading to new insights into the flow dynamics in small-size complex systems with significant implications for the statistical and scaling behaviors of small systems, a topic of great recent interest.

Evolutionary dynamical models for cyclic competitions of three species (e.g., rock, paper, and scissors, or RPS) provide a paradigm, at the microscopic level of individual interactions, to address many issues in coexistence and biodiversity. Real ecosystems often involve competitions among more than three species. By extending the RPS game model to five (rock-paper-scissors-lizard-Spock, or RPSLS) mobile species, we uncover a fundamental type of mesoscopic interactions among subgroups of species. In particular, competitions at the microscopic level lead to the emergence of various local groups in different regions of the space, each involving three species. It is the interactions among the groups that fundamentally determine how many species can coexist. In fact, as the mobility is increased from zero, two transitions can occur: one from a five- to a three-species coexistence state and another from the latter to a uniform, single-species state. We develop a mean-field theory to show that, in order to understand the first transition, group interactions at the mesoscopic scale must be taken into account. Our findings suggest, more broadly, the importance of mesoscopic interactions in coexistence of great many species.

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Understanding the dynamics of human movements is key to issues of significant current interest such as behavioral prediction, recommendation, and control of epidemic spreading. We collect and analyze big data sets of human movements in both cyberspace (through browsing of websites) and physical space (through mobile towers) and find a superlinear scaling relation between the mean frequency of visit〈f〉and its fluctuation σ : σ ∼〈f⟩^β with β ≈ 1.2. The probability distribution of the visiting frequency is found to be a stretched exponential function. We develop a model incorporating two essential ingredients, preferential return and exploration, and show that these are necessary for generating the scaling relation extracted from real data. A striking finding is that human movements in cyberspace and physical space are strongly correlated, indicating a distinctive behavioral identifying characteristic and implying that the behaviors in one space can be used to predict those in the other.

Faced with numerous seemingly intractable social and environmental challenges, many scholars and practitioners are increasingly interested in understanding how to actively engage and transform the existing systems holding such problems in place. Although a variety of analytical models have emerged in recent years, most emphasize either the social or ecological elements of such transformations rather than their coupled nature. To address this, first we have presented a definition of the core elements of a social-ecological system (SES) that could potentially be altered in a transformation. Second, we drew on insights about transformation from three branches of literature focused on radical change, i.e., social movements, socio-technical transitions, and social innovation, and gave consideration to the similarities and differences with the current studies by resilience scholars. Drawing on these findings, we have proposed a framework that outlines the process and phases of transformative change in an SES. Future research will be able to utilize the framework as a tool for analyzing the alteration of social-ecological feedbacks, identifying critical barriers and leverage points and assessing the outcome of social-ecological transformations.

Smart meters, designed for information collection and system monitoring in smart grid, report fine-grained power consumption to utility providers. With these highly accurate profiles of energy usage, however, it is possible to identify consumers' specific activities or behavior patterns, thereby giving rise to serious privacy concerns. This paper addresses these concerns by designing a cost-effective and privacy-preserving energy management technique that uses a rechargeable battery. From a holistic perspective, a dynamic programming framework is designed for consumers to strike a tradeoff between smart meter data privacy and the cost of electricity. In general, a major challenge in solving dynamic programming problems lies in the need for the knowledge of future electricity consumption events. By exploring the underlying structure of the original problem, an equivalent problem is derived, which can be solved by using only the current observations. An online control algorithm is then developed to solve the equivalent problem based on the Lyapunov optimization technique. It is shown that without the knowledge of the statistics of the time-varying load requirements and the electricity price processes, the proposed online control algorithm, parametrized by a positive value V, is within O (1/{V) of the optimal solution to the original problem, where the maximum value of V is limited by the battery capacity. The efficacy of the proposed algorithm is demonstrated through extensive numerical analysis using real data.

Online communities are becoming increasingly important as platforms for large-scale human cooperation. These communities allow users seeking and sharing professional skills to solve problems collaboratively. To investigate how users cooperate to complete a large number of knowledge-producing tasks, we analyze Stack Exchange, one of the largest question and answer systems in the world. We construct attention networks to model the growth of 110 communities in the Stack Exchange system and quantify individual answering strategies using the linking dynamics on attention networks. We identify two answering strategies. Strategy A aims at performing maintenance by doing simple tasks, whereas strategy B aims at investing time in doing challenging tasks. Both strategies are important: empirical evidence shows that strategy A decreases the median waiting time for answers and strategy B increases the acceptance rate of answers. In investigating the strategic persistence of users, we find that users tends to stick on the same strategy over time in a community, but switch from one strategy to the other across communities. This finding reveals the different sets of knowledge and skills between users. A balance between the population of users taking A and B strategies that approximates 2:1, is found to be optimal to the sustainable growth of communities.

Resource allocation takes place in various types of real-world complex systems such as urban traffic, social services institutions, economical and ecosystems. Mathematically, the dynamical process of resource allocation can be modeled as minority games. Spontaneous evolution of the resource allocation dynamics, however, often leads to a harmful herding behavior accompanied by strong fluctuations in which a large majority of agents crowd temporarily for a few resources, leaving many others unused. Developing effective control methods to suppress and eliminate herding is an important but open problem. Here we develop a pinning control method, that the fluctuations of the system consist of intrinsic and systematic components allows us to design a control scheme with separated control variables. A striking finding is the universal existence of an optimal pinning fraction to minimize the variance of the system, regardless of the pinning patterns and the network topology. We carry out a generally applicable theory to explain the emergence of optimal pinning and to predict the dependence of the optimal pinning fraction on the network topology. Our work represents a general framework to deal with the broader problem of controlling collective dynamics in complex systems with potential applications in social, economical and political systems.