Instability helps virtual flies to mate |
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Authors: | Thorsten Hüls |
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Institution: | (1) Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany |
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Abstract: | In this paper we perform a bifurcation analysis for a discrete time dynamical system, describing the behavior of a virtual fly, developed by Böddeker and Egelhaaf (2003). Like real blowflies, the virtual counterparts exhibit a dichotomous behavior: they catch small targets but follow big objects at a constant distance. We consider this model for targets on linear and on circular trajectories. Then we transform the system into a ‘‘frozen’’ form, such that the position of the target is fixed. It turns out that the loss of stability of a fixed point in the frozen system due to a Neimark-Sacker bifurcation, explains the dichotomous behavior of the virtual fly. |
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Keywords: | Discrete time dynamical systems Bifurcation analysis Pursuit behavior of blowflies |
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