Pattern formation, synchronization, and outbreak of biodiversity in cyclically competing games

Wen Xu Wang, Xuan Ni, Ying-Cheng Lai, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

64 Scopus citations


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 the absence of any external control. The waves can emerge from either mixed populations or isolated species in different patches, regardless of the size and the location of the migration target. We also find that, even in a single-species system, target waves can arise from rare mutations, leading to an outbreak of biodiversity. A surprising phenomenon is that target waves in different patches can exhibit synchronization and time-delayed synchronization, where the latter potentially enables the prediction of future evolutionary dynamics. We provide a physical theory based on the spatiotemporal organization of the target waves to explain the synchronization phenomena. We also investigate the basins of coexistence and extinction to establish the robustness of biodiversity through migrations. Our results are relevant to issues of general and broader interest such as pattern formation, control in excitable systems, and the origin of order arising from self-organization in social and natural systems.

Original languageEnglish (US)
Article number011917
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
StatePublished - Jan 27 2011

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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