Mechanisms for oscillations in a biological competition model |
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Authors: | Rodica Curtu |
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Institution: | University of Iowa, Department of Mathematics, 14 MacLean Hall, Iowa City, IA 52242, USA |
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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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