Blar i forfatter "Wikan, Arild"
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An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density - Dependent Survival Probabilities.
Wikan, Arild (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-12-17)A discrete age-structured semelparous Leslie matrix model where density dependence is included both in the fecundity and in the survival probabilities is analysed. Depending on strength of density dependence, we show in the precocious semelparous case that the nonstationary dynamics may indeed be rich, ranging from SYC (a dynamical state where the whole population is in one age class only) dynamics ... -
An analysis of Discrete stage-structured prey and prey-predator population models.
Wikan, Arild (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-04-16)Discrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand are permanent (i.e., the population will neither go extinct nor exhibit explosive oscillations) and, moreover, that the transfer from stability to nonstationary behaviour always goes through a supercritical Neimark−Sacker bifurcation.The prey model covers species that ... -
Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest
Wikan, Arild; Kristensen, Ørjan (Journal article; Tidsskriftartikkel; Peer reviewed, 2021-01-11)Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that ... -
Dynamical consequences of reproductive delay in Leslie Matrix Models with nonlinear survival probabilities
Wikan, Arild (Research report; Forskningsrapport, 1998) -
From chaos to chaos : an analysis of a discrete age-structured prey-predator model
Wikan, Arild (Research report; Forskningsrapport, 2000) -
An introduction to discrete dynamical systems
Wikan, Arild (Research report; Forskningsrapport, 2007) -
Nonstationary and Chaotic Dynamics in Age-Structured Population Models
Wikan, Arild; Kristensen, Ørjan (Journal article; Tidsskriftartikkel; Peer reviewed, 2017-08-06)The dynamics from nonlinear discrete age-structured population models is under consideration. Focus is on bifurcations, as well as nonstationary and chaotic dynamics. We also explore different mechanisms which may lead to periodic phenomena. Some new results are also presented, in particular from models where both fecundity and survival terms contain nonlinear elements. -
On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models
Wikan, Arild (Journal article; Tidsskriftartikkel; Peer reviewed, 2015-06-17)By use of a nonlinear stage-structured population model the role of cannibalism and the combined role of cannibalism and harvest have been explored. Regarding the model, we prove that in most parts of parameter space it is permanent. We also show that the transfer from stability to nonstationary dynamics always occurs when the unique stable equilibrium undergoes a supercritical Neimark-Sacker (Hopf) ... -
Optimal Selection and Effort in a Fishery on a Stock with Cannibalistic Behaviour : The Case of the Northeast Arctic Cod Fisheries
Eide, Arne; Wikan, Arild (Journal article; Tidsskriftartikkel; Peer reviewed, 2010)We explore a fishery targeting the mature part of a stock, while bycatching the immature part. Both targeted catch and bycatch may have positive market values. Cost of effort is supposed to be a function of the selection properties of the fishing gears. Mature fish is assumed to cannibalise on the immature part of the stock. A bioeconomic model of the problem is set up and it is shown that the model ... -
Periodic phenomena in a discrete age-structured prey-predator model : I density dependant survival probalities
Wikan, Arild (Research report; Forskningsrapport, 1999) -
Prey-Predator Interactions in Two and Three Species Population Models
Wikan, Arild; Kristensen, Ørjan (Journal article; Tidsskriftartikkel; Peer reviewed, 2019-02-17)Discrete nonlinear two and three species prey-predator models are considered. Focus is on stability and nonstationary behaviour. Regarding the two species model, depending on the fecundity of the predator, we show that the transfer from stability to instability goes through either a supercritical flip or a supercritical Neimark-Sacker bifurcation and moreover that there exist multiple attractors in ... -
Semelparity versus Iteroparity : an analysis of a stage-structured population model
Wikan, Arild (Research report; Forskningsrapport, 2008) -
Stage-Dependent Predation on Prey Species Who Possess Different Life Histories
Wikan, Arild; Kristensen, Ørjan Fosdahl (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-03-24)Two stage-structuredone-population (prey) models together with four prey-predator models are analyzed. Regarding the prey models, where one of them has fecundity elements which depend on the total population while the fecundities of the other depend on the mature part of the population only, we prove that both of them are permanent and moreover that their fixed points undergo supercritical bifurcations, ... -
Towards some general ecological principles
Wikan, Arild (Journal article; Tidsskriftartikkel; Peer reviewed, 2013-01-03)Discrete deterministic age-structured, stage-structured and difference delay equation population models are analysed and compared with respect to stability and nonstationary behaviour. All three models show that species with iteroparous life histories tend to be more stable than species with semelparous life histories which allow us to conclude that this must be a fairly general ecological ...