An analysis of a nonlinear stage-structured cannibalism model with application to the Northeast Arctic cod stock

Wikan, Arild; Eide, Arne

doi:10.1016/j.bulm.2004.03.005

Cited by 20 publications

(30 citation statements)

References 17 publications

(12 reference statements)

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“…While increased recruitment may give birth to chaotic oscillations, there is a tendency that increased cannibalism seems to stabilize the dynamics but not always (cf. the discussion in [10][11][12][13][14]). Finally, change in fishing patterns may also influence the dynamics as accounted for in [9,15,16].…”

Section: Introductionmentioning

confidence: 97%

On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models

Wikan¹

2015

Journal of Marine Biology

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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) bifurcation. Moreover, the dynamic consequences of catch depend not only on which part of the population (immature or mature) is exposed to increased harvest pressure but also on which part of the immature population (newborns, older immature individuals) suffers from cannibalism. Indeed, if only newborns are exposed to cannibalism an enlargement of harvest pressure on the mature part of the population may act in a stabilizing fashion. On the other hand, whenever the whole immature population is exposed to cannibalism there are parts in parameter space where increased harvest on the mature population acts in a destabilizing fashion.

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Section: Introductionmentioning

confidence: 97%

On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models

Wikan¹

2015

Journal of Marine Biology

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“…Its effects on population dynamics are vast and complex [8]. Cannibalism on the one hand can be an effective mechanism for the regulation and equilibration of population size [10,25]. Cannibalism on the other hand has also been found to promote population oscillations [13,15].…”

Section: Discussionmentioning

confidence: 99%

“…This population interaction results in a predator-prey system with the prey population being cannibalistic. There are many existing mathematical models in the literature including partial/ordinary differential equations and difference equations with different modeling assumptions exploring cannibalism [3,[5][6][7]9,10,[13][14][15]25]. It has been concluded in these mathematical models that cannibalism can have important effects on population dynamics.…”

Section: Introductionmentioning

confidence: 99%

Cannibalism in discrete-time predator–prey systems

Chow

Jang

2012

Journal of Biological Dynamics

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In this study, we propose and investigate a two-stage population model with cannibalism. It is shown that cannibalism can destabilize and lower the magnitude of the interior steady state. However, it is proved that cannibalism has no effect on the persistence of the population. Based on this model, we study two systems of predator-prey interactions where the prey population is cannibalistic. A sufficient condition based on the nontrivial boundary steady state for which both populations can coexist is derived. It is found via numerical simulations that introduction of the predator population may either stabilize or destabilize the prey dynamics, depending on cannibalism coefficients and other vital parameters.

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“…Particularly in fishery models, this has often been motivated by the assumption that most density effects are present only in the first year of life. Examples of theoretical studies which deal with nonstationary and chaotic behaviour as well as behaviour linked to concrete species may be found in [1][2][3][4][5][6][7]. In case of ergodic properties we refer to [8][9][10]; see also [11].…”

Section: Introductionmentioning

confidence: 99%

An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density-Dependent Survival Probabilities

Wikan¹

2017

Journal of Applied Mathematics

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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 to cycles of low period where all age classes are populated. Quasiperiodic and chaotic dynamics have also been identified. Moreover, outside parameter regions where SYC dynamics dominates, we prove that the transfer from stability to instability goes through a supercritical Neimark−Sacker bifurcation, and it is further shown that when the population switches from possessing a precocious to a delayed semelparous life history both stability properties and the possibility of periodic dynamics become weaker.

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An analysis of a nonlinear stage-structured cannibalism model with application to the Northeast Arctic cod stock

Cited by 20 publications

References 17 publications

On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models

On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models

Cannibalism in discrete-time predator–prey systems

An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density-Dependent Survival Probabilities

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