The Influence of Temporal Migration in the Synchronization of Populations
DOI:
https://doi.org/10.5540/tema.2015.016.01.0031Abstract
A discrete metapopulation model with temporal dependent migration is proposed in order to study the stability of synchronized dynamics. During each time step, we assume that there are two processes involved in the population dynamics: local patch dynamics and migration process between the patches that compose the metapopulation. We obtain an analytical criterion that depends on the local patch dynamics (Lyapunov number) and on the whole migration process. The stability of synchronized dynamics depends on how individuals disperse among the patches.References
J.C. Allen, W.M. Schauer, D. Rosko, Chaos reduces species extinction by amplifying local population noise, Nature 364, (1993), 229-232.
B. Blasius, A. Huppert, L. Stone, Complex dynamics and phase synchronization in saptially extended ecological systems, Nature 399, (1999), 353-359.
M. Doebeli, Dispersal and Dynamics, Theor. Pop. Biol. 47 (1995) 82-106.
D.J., Earn, S.A. Levin, P. Rohani, Coherence and Conservation, Science 290, (2000), 1360-1364.
J.P. Eckmann, D. Ruelle, Ergodic Theory of chaos and strange attractors, Rev. Modern Phys. 57, (1985), 617-656.
L., Hansson, Dispersal and connectivity in metapopulations, Biol. J. Linn. Soc. 42 (1991) 89-103.
M. Heino, V. Kaitala, E. Ranta, J. Lindström, Synchronous dynamics and rates of extinction in spatially structured populations, Proc. R. Soc. London B 264, (1997) 481-486.
R. A. Ims, H. P. Andreassen, Spatial synchronization of vole population dynamics by predatory birds, Nature 408, (2000) 194-196.
P. Lancaster, M. Tismenetsky, The Theory of Matrices, Academic Press, London, 1985.
R. M., May, Biological populations with nonoverlapping generations: stable points, stable cycles, and chaos, Science 186 (1974), 645-647.
R. M. May, A. L. Lloyd, Synchronicity, chaos and population cycles: spatial coherence in an uncertain world, Trends Ecol. Evol., 14 (1999), 417-418.
J. A. L. Silva, M. L. De Castro, D.A.R. Justo, Synchronism in a metapopulation model. Bull. Math. Biol. 62, (2000), 337-349.
J.A.L. Silva, F.T. Giordani, Density-dependent migration and synchronism in metapopulations, Bull. Math. Biol., 68, (2006), 451-465.
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