A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME

Hüls T (2008)
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 18(7): 1957-1972.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
In this paper, we extend the two-dimensional discrete time model of the virtual fly, developed by Boddeker and Egelhaaf [2003], into three space dimensions, and introduce its continuous time analog. Like real blowflies, the virtual counterparts exhibit a dichotomous chasing behavior: depending on size, velocity and the course of the targets; they catch the targets or pursue them at constant distance. Here, we analyze this behavioral characteristic with respect to the course of the target, in particular, we choose trajectories, spiraling upwards. After setting up the three-dimensional model, we transform it into the local coordinates of the pursuer, using equivariance properties. Then bifurcation tools apply, and it turns out that depending on the gradient and the curvature of the spiraling trajectory, a fixed point in the transformed system can lose or gain stability. A stable fixed point corresponds in the original system to a trajectory, on which the virtual fly follows the target at a constant distance. In this way, we explain the dichotomous behavior through the occurrence of bifurcations.
Stichworte
equivariant systems; pursuit behavior of blowflies; Bifurcation analysis
Erscheinungsjahr
2008
Zeitschriftentitel
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Band
18
Ausgabe
7
Seite(n)
1957-1972
ISSN
0218-1274
Page URI
https://pub.uni-bielefeld.de/record/1586046

Zitieren

Hüls T. A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 2008;18(7):1957-1972.
Hüls, T. (2008). A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 18(7), 1957-1972.
Hüls, T. (2008). A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 18, 1957-1972.
Hüls, T., 2008. A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 18(7), p 1957-1972.
T. Hüls, “A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME”, INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, vol. 18, 2008, pp. 1957-1972.
Hüls, T.: A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS. 18, 1957-1972 (2008).
Hüls, Thorsten. “A BIFURCATION ANALYSIS OF A 3D BLOWFLY MODEL IN DISCRETE AND CONTINUOUS TIME”. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS 18.7 (2008): 1957-1972.

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