• Controlling complex networks
• Reconstructing complex networks and dynamics from time series
• Modeling and predicting human mobility patterns                    
• Evolutionary games on spatial networks

Controlling complex networks is of paramount importance in science and engineering. Despite the recent development of structural controllability theory, we continue to lack a framework to control undirected complex networks, especially given link weights. Here we introduce an exact controllability paradigm based on the maximum multiplicity to identify the minimum set of driver nodes required to achieve full control of networks with arbitrary structures and link-weight distributions. The framework reproduces the structural controllability of directed networks characterized by structural matrices. We explore the controllability of a large number of real and model networks, finding that dense networks with identical weights are difficult to be controlled. An efficient and accurate tool is offered to assess the controllability of large sparse and dense networks. The exact controllability framework enables a comprehensive understanding of the impact of network properties on controllability, a fundamental problem towards our ultimate control of complex systems.

The exact controllability criterion is published in Nature Communications in 2013, see here. We are continuously working on the fundamental problem of controlling complex networks by using the theoretical tools we have developed. Indeed, the tool allows us to explore many interesting problems beyond the structural controllability.

We developed a general paradigm based on compressive sensing theory to reconstruct complex networked systems and nonlinear dynamical equations by from extremely short time series. We have applied the famework to chaotic systems, see here, to reconstruct propagation networks and identify hidden sources, see here, to reconstructing interactions in evolutionary games, see here, to ascertaining and inferring hidden nodes, see here, to forecasting synchronization of coupled chaotic oscillators, see here. Our novel scheme can have many more applications in spreading networks, regulation networks, cascading processes and etc.

The most striking characteristics of our method are the extremely low requirement of measurement data and the perfect reconstruction accuracy, resulting from the compressive sensing theory. Our main contribution lies in casting the inverse problem of complex networks into the sparse signal reconstruction, which can be addresed by exploiting the powerful conpressive sensing algorithm. Our approach has implications in a wide range of fields pertaining to complex networks and complex systems, ranging from social to physical and biological context. The series of approaches have been published in Nature Communications, Phys. Rev. Lett., Phys. Rev. X and etc.

Cooperative behaviors ubiquitous in nature and society somewhat contradict to the Darwin's theory in that selfish behaviors usually gain more profits from the competition with altruistic behaviors, such that suppose to prevail during the evolution of species. So far, tremendous efforts have been dedicated to address the puzzle of nature. We attempt to explain the emergence and persistence of cooperation among selfish individuals by incorporating the network science.

We have discoverd several natural mechanisms that facilate cooperative behaviors, including memory-based strategy updating, see here, adaptive migration, see here, coevolving time scale, see here, diversity, see here, asymmetric cost, see here, dynamical and structural randomness, see here, and connection density, see here. In particular, we found that the presence of death induced by low payoffs can trigger an avalanche process, rendering the elimination of defectors and a pure cooperative environment, see here. For some specific rule of strategy updating, there exhibits hysteresis loop in the cooperation level, suggesting the existence of bistate states, in analogy with that in nonlinear dynamics, see here.

Biodiversity is ubiquitous in nature and fundamental to evolution in ecosystems. However, a significant challenge remains in understanding biodiversity since, by the principle of natural selection, only fitter species are supposed to be capable of surviving from interactions and competitions with other species for limited resources. Evolutionary game theory has been used as a paradigm to address the coexistence of competing species, which is the key to sustaining biodiversity.

Species in nature are typically mobile over diverse distance scales, examples of which range from bacteria run to long-distance animal migrations. These behaviors can have a significant impact on biodiversity. Addressing the role of migration in biodiversity microscopically is fundamental but remains a challenging problem in interdisciplinary science. We incorporate both intra- and inter-patch migrations in stochastic games of cyclic competitions and find that the interplay between the migrations at the local and global scales can lead to robust species coexistence characterized dynamically by the occurrence of remarkable target-wave patterns. In a broad range of parameter space, target waves at different patches exhibit synchronizeation and time-delayed synchronization, stablizing the coexsitence of three species with cyclic competitions, see here. We have also found plane waves in spatial Rock-Paper-Scissors games, see here, basin of attraction and extinction, see here, the dual effect of epidemic spreading on species coexistence, see here, and multi-armed spirals and multi-pair antispirals in spatial Rock-Paper-Scissors games consisting of mobile populations, see here.