Sincronização em Metapopulações com Hierarquia na Dinâmica Local
DOI:
https://doi.org/10.5540/tema.2007.08.02.0249Abstract
Neste trabalho investigamos a possibilidade de órbitas caóticas oscilarem de forma sincronizada em modelos metapopulacionais de k espécies submetidos a migração dependente da densidade. Consideramos a dinâmica local de forma hierárquica e obtemos um critério para a estabilidade do estado sincronizado de órbitas caóticas sincronizadas.References
[1] J.C. Allen, W.M. Schaffer, D. Rosko, Chaos reduces species extinction by amplifying local population noise, Nature, 364 (1993), 229-232.
J. Best, C. Castillo-Chavez, A-A. Yakubu, Hierarchical Competition in Discrete Time Models with Dispersal, Fields Institutional of Communications, 36 (2003), 59-86.
C. Castillo-Chavez, A-A. Yakubu, Discrete time S-I-S models with complex dynamics, Nonlinear Analysis, 47 (2001), 4753-4762.
H. N. Comins, The spatial dynamics of host-parasitoid systems, J. Anim. Ecol., 61 (1992), 735-748.
M.L. de Castro, J.A.L. Silva, D.A.R. Justo, Stability in an-structured metapopulation model, J. Math. Biology, 52 (2006) 183-208.
L. Dieci, E.S. Van Vleck, Computation of a few Lyapunov exponents for continuous and discrete dynamical systems, Appl. Numer. Math., 17 (1995), 275-291.
M. Ding, W. Yang, Stability of synchronous and on-off intermittency in coupled map lattices, Physical Review E, 56 (1997), 4009-4016.
A.S. Dmitriev, M. Shirokov, S.O. Starkov, Chaotic synchronization in ensembles of coupled maps, IEEE Transactions on Circuits and Systems- : Fundamental Theory and Applications, 44 (1997), 918-926.
D.J.D. 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, Am. Physical Society, 57 (1985), 617-656.
A. Gonzalez, J. H. Lawton, F. S. Gilbert, T. M. Blackburn, I. Evans-Freke, Metapopulation dynamics, abundance, and distribution in a microsystem, Science, 281 (1998), 2045-2047.
M.P. Hassell, H.N. Comins, R.M. May, Spatial structure and chaos in insect population dynamics, Nature, 353 (1991), 255-258.
M. Heino, V. Kaitala, E. Ranta, J. Lindstr¨om, Synchonous dynamics and rates of extinction in spatially structured populations, Proc. Royal Soc. London B, 264 (1997), 481-486.
R.A. Ims, H.P. Andreassen, Density-dependent dispersal and spatial population dynamics, Proc. Roy. Soc. B, 272 (2005) 913-918.
V.A.A. Jansen, A.L. Lloyd, Local stability analysis of spatially homogeneous solutions of multi-patch systems, J. Math. Biol., 41 (2000), 232-252.
A.L. Lloyd, V.A.A. Jansen, Spatiotemporal dynamics of epidemics: synchrony in metapopulation models, Math. Biosc., 188 (2004), 1-16.
P. Lancaster, M. Tismenetsky, “The Theory of Matrices”, Academic Press, London, 1985.
S.A. Levin, C.P. Goodyear, Analysis of an age-structured fishery model, J. Math. Biol., 9 (1980), 245-274.
A. Pikovsky, M. Rosenblum, J. Kurths, “Synchronization: a universal concept in nonlinear sciences”, Cambridge University Press, Cambridge, 2001.
P. Rohani, R.M. May, M.P. Hassell, Metapopulation and equilibrium stability: the effects of spatial structure, J. Theor. Biol. , 181 (1996), 97-109.
G. Sansone, R. Conti, “Non-Linear Differential Equations”, The Macmillan Company, New York, 1964.
J.A.L. Silva, J.A. Barrionuevo, F.T. Giordani, Synchronism in populations networks with non linear coupling, submetido, 2006.
J.A.L. Silva, M.L.D. Castro, D.A.R. Justo, Stability in a metapopulation model with density-dependent dispersal, Bull. Math. Biol., 63 (2001), 485-506.
J.A.L. Silva, M.L.D. 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.
J.A.L. Silva, T.G. Hallam, Compensation and stability in nonlinear matrix models, Math. Bios., 31 (1992), 67-101.
R.V. Solé, J.P.G. Gamarra, Chaos, dispersal and extinction in coupled ecosystems, J. Theor. Biol., 193 (1998), 539-541.
P. Walters, “An Introduction to Ergodic Theory”, Springer, New York, 1982.
A. Wikan, E. Mjølhus, Periodicity of 4 in Age-structured population models with density dependence, J. Theor. Biol., 173 (1995), 109-119.
Downloads
Published
How to Cite
Issue
Section
License
Copyright
Authors of articles published in the journal Trends in Computational and Applied Mathematics retain the copyright of their work. The journal uses Creative Commons Attribution (CC-BY) in published articles. The authors grant the TCAM journal the right to first publish the article.
Intellectual Property and Terms of Use
The content of the articles is the exclusive responsibility of the authors. The journal uses Creative Commons Attribution (CC-BY) in published articles. This license allows published articles to be reused without permission for any purpose as long as the original work is correctly cited.
The journal encourages Authors to self-archive their accepted manuscripts, publishing them on personal blogs, institutional repositories, and social media, as long as the full citation is included in the journal's website version.