ICIAM07 Contributed Papers

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Mechanisms for oscillations in a biological competition model

  1. Rodica Curtu1,2,*

Article first published online: 6 AUG 2008

DOI: 10.1002/pamm.200700331

Issue

PAMM

PAMM

Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Zürich 2007

Volume 7, Issue 1, pages 2030019–2030020, December 2007

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How to Cite

Curtu, R. (2007), Mechanisms for oscillations in a biological competition model. PAMM, 7: 2030019–2030020. doi: 10.1002/pamm.200700331

Author Information

  1. 1

    University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA 52242, USA

  2. 2

    Transilvania University of Brasov, Romania

*Phone: +1 319 335 0744, Fax: +1 319 335 0627

Publication History

  1. Issue published online: 6 AUG 2008
  2. Article first published online: 6 AUG 2008

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Abstract

A four-dimensional dynamical system that models perceptual bistability in the brain is analyzed. Two variables represent the activity of two competing neural populations and they evolve in fast time; other two variables are slow and they are associated with an intrinsic negative feedback to each population. The external stimulus strength I is the bifurcation parameter. We construct the normal form and prove that oscillations occur in the system through supercritical Hopf bifurcations: as I decreases from large to moderate values a limit cycle is born; then it disappears for lower values of I. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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