Gunnar Söderbacka

Gunnar Söderbacka
Åbo Akademi University · Department of Natural Sciences

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29
Publications
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239
Citations

Publications

Publications (29)
Preprint
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In this note we derive simple analytical approximations for the solutions of x − log x = y − log y and use them for estimating trajectories following Lotka-Volterra-type integrals. We show how our results imply estimates for the Lambert W function as well as for trajectories of general predator-prey systems, including e.g. Rosenzweig McArthur equat...
Article
This work contains a review of some important results on a known two predators - one prey system. We also add essential new numerical results on multiple attractors. We consider the case when the predators coexist. We distinguish two possibilities. The first is when the dynamics is well described by the dynamics of a one dimensional map. We discuss...
Preprint
Full-text available
In this paper, we study the classical two-predators-one-prey model. The classical model described by a system of 3 ordinary differential equations can be reduced to a one-dimensional bimodal map. We prove that this map has at most two stable periodic orbits. Besides, we describe the structure of bifurcations of the map. Taking this mechanism into a...
Presentation
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In this presentation we make a review of the behaviour of a known system of many predators and one prey. We mainly consider the case with two predators. We consider the question below and give results and formulate open problems. • Extinction conditions for one predator • Different types of coexistence • Usual period-doubling leading to chaos, when...
Article
Full-text available
In this paper, we consider a family of systems with two predators feeding on one prey. We show how to construct a positively invariant set in which it is possible to define a Poincaré map for examining the behavior of the system, mainly in the case when both predators survive. We relate it to examples from earlier works.
Article
Full-text available
We consider a Rosenzweig–MacArthur predator-prey system which incorporateslogisticgrowthofthepreyintheabsenceofpredatorsandaHollingtypeIIfunctionalresponsefor 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...
Preprint
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 estimate...
Preprint
In this paper we consider a family of system with 2 predators feeding on one prey. We show how to construct a positively invariant set in which it is possible to define a Poincar\'e map for examining the behaviour of the system, mainly in the case when both predators survive. We relate it to examples from earlier works.
Article
Full-text available
Questions: Assuming that arctic lemming oscillations are generated by interactions between lemmings and depletable plants, how should these oscillations change in response to varying densities of marine-subsidized predators and differences in the production of herbaceous forage? Are the patterns thus generated consistent with existing data? Feature...
Article
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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 descri...
Article
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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 coupl...
Article
Full-text available
In this paper we formally prove that invading carnivores in the discrete food-chain derived and preliminary analyzed in [2] always makes the system less stable and thus, limit the food-chain length in the corresponding system. Hence, invading unsaturated carnivores are not able to stabilize oscillatory dynamics. What we prove constitutes a signific...
Article
Full-text available
In this paper we find the possible phase portraits and bifurcations for a general class of host-vector epidemic models with non-linear incidence function generalizing the Ross model.

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