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Stationary pattern formation in a discrete excitable system with strong inhibitory coupling

Naoko Kurata1, Hiroyuki Kitahata1, Hitoshi Mahara2, Atsushi Nomura3, Hidetoshi Miike4, and Tatsunari Sakurai1

  • 1Graduate School of Science, Chiba University, Chiba 263-8522, Japan
  • 2Nanotechnology Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba 305-8565, Japan
  • 3Faculty of Education, Yamaguchi University, Yamaguchi 753-8513, Japan
  • 4Faculty of Engineering, Yamaguchi University, Ube 755-8611, Japan

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Phys. Rev. E 79, 056203 – Published 5 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.056203

Abstract

We study a discrete model described by coupled excitable elements following the monostable FitzHugh-Nagumo equations. Our model has a weakly coupled activator and a strongly coupled inhibitor. For two-coupled excitable elements, we show that the trivial state always exists stably, while nontrivial stable states appear depending on the coupling strengths. In a one-dimensional array, only the elements near the initial condition step remain at nontrivial states. We discuss stationary pattern formation in a one-dimensional array and a two-dimensional lattice using the analytical results of a two-coupled system.

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Phys. Rev. E 79, 056203– Published 5 May, 2009
  • Received 25 December 2008

© 2009 American Physical Society

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