Pattern formations driven by cyclic interactions: A brief review of recent developments

¹ Institute of Technical Physics and Materials Science, Centre for Energy Research, Hungarian Academy of Sciences P.O. Box 49, H-1525 Budapest, Hungary
² Departamento de Física, Universidade Estadual de Maringá - 87020-900 Maringá, PR, Brazil
³ Departamento de Física, Universidade Federal da Paraíba - 58051-970 João Pessoa, PB, Brazi

Received: 13 August 2020
Accepted: 31 August 2020

Abstract

Lotka's seminal work (Lotka A. J., Proc. Natl. Acad. Sci. U.S.A., 6 (1920) 410) “on certain rhythmic relations” is already one hundred years old, but the research activity about pattern formations due to cyclical dominance is more vibrant than ever. It is because non-transitive interactions have a paramount role on maintaining biodiversity and adequate human intervention into ecological systems requires a deeper understanding of the related dynamical processes. In this Perspective we overview different aspects of biodiversity, with focus on how it can be maintained based on mathematical modeling of the last years. We also briefly discuss the potential links to evolutionary game models of social systems, and finally, give an overview about potential prospects for future research.