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- Gyllenberg, M., et al.
(författare)
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Bifurcation analysis of a metapopulation model with sources and sinks
- 1996
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Ingår i: Journal of nonlinear science. - 0938-8974 .- 1432-1467. ; 6:4, s. 329-366
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Tidskriftsartikel (refereegranskat)abstract
- A class of functions describing the Allee effect and local catastrophes in population dynamics is introduced and the behaviour of the resulting one-dimensional discrete dynamical system is investigated in detail. The main topic of the paper is a treatment of the two-dimensional system arising when an Allee function is coupled with a function describing the population decay in a so-called sink. New types of bifurcation phenomena are discovered and explained. The relevance of the results for metapopulation dynamics is discussed.
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- Gyllenberg, Mats, et al.
(författare)
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Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model
- 1993
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Ingår i: Mathematical Biosciences. - : Elsevier BV. - 0025-5564 .- 1879-3134. ; 118:1, s. 25-49
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Tidskriftsartikel (refereegranskat)abstract
- A discrete model for a metapopulation consisting of two local populations connected by migration is described and analyzed. It is assumed that the local populations grow according to the logistic law, that both populations have the same emigration rate, and that migrants choose their new habitat patch at random. Mathematically this leads to a coupled system of two logistic equations. A complete characterization of fixed point and two-periodic orbits is given, and a bifurcation analysis is performed. The region in the parameter plane where the diagonal is a global attractor is determined. In the symmetric case, where both populations have the same growth rate, the analysis is rigorous with complete proofs. In the nonsymmetric case, where the populations grow at different rates, the results are obtained numerically. The results are interpreted biologically. Particular attention is given to the sense in which migration has a stabilizing and synchronizing effect on local dynamics.
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- Lindström, Torsten, 1965-, et al.
(författare)
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On the stability-complexity relation for unsaturated semelpareous discrete food-chains
- 2011
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Ingår i: Studies in mathematical sciences. - 1923-8444 .- 1923-8452. ; 2:1, s. 157-182
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we formally prove that invading carnivores in thediscrete food-chain derived and preliminary analyzed inLindström (2002) always makes thesystem less stable and thus, limit the food-chain length in thecorresponding system. Hence, invading unsaturated carnivores arenot able to stabilize oscillatory dynamics.What we prove constitutes a significant difference betweendiscrete and continuous food-chains. Actually, Freedman andWaltman (1977) related the stabilizingproperties of an invading carnivore in continuous food-chains to absence of saturation: An unsaturated carnivore keeps at least oneinterior equilibrium - if one exists - locally stable.One consequence is that the dynamics of unsaturated discretefood-chains display similarities with saturated continuousfood-chains. Indeed, discrete dynamics seem to have a similardestabilizing impact on the dynamics as saturation has.
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- Lundström, Niklas, 1980-, et al.
(författare)
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Estimates of size of cycle in a predator-prey system
- 2022
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Ingår i: Differential Equations and Dynamical Systems. - : Springer. - 0971-3514 .- 0974-6870. ; 30:1, s. 131-159
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Tidskriftsartikel (refereegranskat)abstract
- We consider a Rosenzweig–MacArthur predator-prey system which incorporates logistic growth of the prey in the absence of predators and a Holling type II functional response for interaction between predators and preys. We assume that parameters take values in a range which guarantees that all solutions tend to a unique limit cycle and prove estimates for the maximal and minimal predator and prey population densities of this cycle. Our estimates are simple functions of the model parameters and hold for cases when the cycle exhibits small predator and prey abundances and large amplitudes. The proof consists of constructions of several Lyapunov-type functions and derivation of a large number of non-trivial estimates which are of independent interest.
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