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.

Deposits of dark material appear on Vesta’s surface as features of relatively low-albedo in the visible wavelength range of Dawn’s camera and spectrometer. Mixed with the regolith and partially excavated by younger impacts, the material is exposed as individual layered outcrops in crater walls or ejecta patches, having been uncovered and broken up by the impact. Dark fans on crater walls and dark deposits on crater floors are the result of gravity-driven mass wasting triggered by steep slopes and impact seismicity. The fact that dark material is mixed with impact ejecta indicates that it has been processed together with the ejected material. Some small craters display continuous dark ejecta similar to lunar dark-halo impact craters, indicating that the impact excavated the material from beneath a higher-albedo surface. The asymmetric distribution of dark material in impact craters and ejecta suggests non-continuous distribution in the local subsurface. Some positive-relief dark edifices appear to be impact-sculpted hills with dark material distributed over the hill slopes.

Dark features inside and outside of craters are in some places arranged as linear outcrops along scarps or as dark streaks perpendicular to the local topography. The spectral characteristics of the dark material resemble that of Vesta’s regolith. Dark material is distributed unevenly across Vesta’s surface with clusters of all types of dark material exposures. On a local scale, some craters expose or are associated with dark material, while others in the immediate vicinity do not show evidence for dark material. While the variety of surface exposures of dark material and their different geological correlations with surface features, as well as their uneven distribution, indicate a globally inhomogeneous distribution in the subsurface, the dark material seems to be correlated with the rim and ejecta of the older Veneneia south polar basin structure. The origin of the dark material is still being debated, however, the geological analysis suggests that it is exogenic, from carbon-rich low-velocity impactors, rather than endogenic, from freshly exposed mafic material or melt, exposed or created by impacts.

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.