Biological Cybernetics

, Volume 113, Issue 1–2, pp 61–70 | Cite as

Controlling excitable wave behaviors through the tuning of three parameters

  • Sayak Bhattacharya
  • Pablo A. IglesiasEmail author


Excitable systems are a class of dynamical systems that can generate self-sustaining waves of activity. These waves are known to manifest differently under diverse conditions, whereas some travel as planar or radial waves, and others evolve into rotating spirals. Excitable systems can also form stationary stable patterns through standing waves. Under certain conditions, these waves are also known to be reflected at no-flux boundaries. Here, we review the basic characteristics of these four entities: traveling, rotating, standing and reflected waves. By studying their mechanisms of formation, we show how through manipulation of three critical parameters: time-scale separation, space-scale separation and threshold, we can interchangeably control the formation of all the aforementioned wave types.


Excitable systems Wave propagation Spiral waves Standing waves Wave reflection 



This review arose as a consequence of a workshop on the control of cellular and molecular systems at the Mathematical Biosciences Institute at The Ohio State University, which receives major funding from the National Science Foundation Division of Mathematical Sciences. We are grateful to Yuchuan Miao, Marc Edwards and Peter Devreotes for fruitful conversations and collaboration on wave propagation in migratory cells.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringThe Johns Hopkins UniversityBaltimoreUSA

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