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Migratory dynamics of interacting subpopulations: Regular and chaotic behavior
Author(s) -
Reiner Rolf,
Munz Martin,
Weidlich Wolfgang
Publication year - 1988
Publication title -
system dynamics review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 57
eISSN - 1099-1727
pISSN - 0883-7066
DOI - 10.1002/sdr.4260040110
Subject(s) - attractor , chaotic , statistical physics , lyapunov exponent , nonlinear system , limit (mathematics) , fractal , dynamics (music) , fractal dimension , computer science , dimension (graph theory) , coupled map lattice , motion (physics) , complex dynamics , mathematics , mathematical analysis , control theory (sociology) , physics , pure mathematics , control (management) , synchronization of chaos , artificial intelligence , quantum mechanics , acoustics
Abstract We demonstrate that different kinds of dynamic behavior may occur in a general migration system. The deterministic nonlinear coupled mean value equations are introduced. The intergroup and intragroup interactions of the subpopulations determine the dynamics of the system. First, the route to chaotic motion in the case of two subpopulations migrating between three regions is briefly presented. In the special case of three interacting sub‐populations migrating between three regions, we then show in detail that all kinds of attractors (fixed points, limit cycles, and strange attractors) exist. Characteristics of the motion, namely the Fourier spectrum, Lyapunov exponents, and the fractal dimension of the attractors, are analyzed. Finally, we discuss the relevance of the results for real migration systems.