Turing patterns in simplicial complexes.

The spontaneous emergence of patterns in nature, such as stripes and spots, can be mathematically explained by reaction-diffusion systems. These patterns are often referred as Turing patterns to honor the seminal work of Alan Turing in the early 1950s. With the coming of age of network science, and with its related departure from diffusive nearest-neighbor interactions to long-range links between nodes, additional layers of complexity behind pattern formation have been discovered, including irregular spatiotemporal patterns.

Impacts of climate change on vegetation pattern: Mathematical modeling and data analysis.

Climate change has become increasingly severe, threatening ecosystem stability and, in particular, biodiversity. As a typical indicator of ecosystem evolution, vegetation growth is inevitably affected by climate change, and therefore has a great potential to provide valuable information for addressing such ecosystem problems. However, the impacts of climate change on vegetation growth, especially the spatial and temporal distribution of vegetation, are still lacking of comprehensive exposition.

Epidemic Spreading in Metapopulation Networks Coupled With Awareness Propagation.

Understanding the feedback loop that links the spatiotemporal spread of infectious diseases and human behavior is an open problem. To study this problem, we develop a multiplex framework that couples epidemic spreading across subpopulations in a metapopulation network (i.e.

Optimal control of the reaction-diffusion process on directed networks.

Reaction-diffusion processes organized in networks have attracted much interest in recent years due to their applications across a wide range of disciplines. As one type of most studied solutions of reaction-diffusion systems, patterns broadly exist and are observed from nature to human society. So far, the theory of pattern formation has made significant advances, among which a novel class of instability, presented as wave patterns, has been found in directed networks.

Optimal control of networked reaction-diffusion systems.

Patterns in nature are fascinating both aesthetically and scientifically. Alan Turing's celebrated reaction-diffusion model of pattern formation from the 1950s has been extended to an astounding diversity of applications: from cancer medicine, via nanoparticle fabrication, to computer architecture. Recently, several authors have studied pattern formation in underlying networks, but thus far, controlling a reaction-diffusion system in a network to obtain a particular pattern has remained elusive.

Optimal control of pattern formations for an SIR reaction-diffusion epidemic model.

Patterns arising from the reaction-diffusion epidemic model provide insightful aspects into the transmission of infectious diseases. For a classic SIR reaction-diffusion epidemic model, we review its Turing pattern formations with different transmission rates. A quantitative indicator, "normal serious prevalent area (NSPA)", is introduced to characterize the relationship between patterns and the extent of the epidemic.