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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 10. |
- Söderbacka, Gunnar, et al.
(författare)
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The effect of resistance of lines of electric transmissions on the work of the system "synchronous generator"
- 1997
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Ingår i: St Petersburg University Mechanics Bulletin. - 0883-623X. ; :3, s. 5-7
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Tidskriftsartikel (refereegranskat)abstract
- It is shown that the resistance of supply line essentially affects the work of an asynchronous motor by abruptly decreasing its maximally possible moment on the rotor's axis. It does not practically affect the generator. Since the found critical resistance is comparatively small, it is necessary to take into account only if the supply line is sufficiently long.
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