Dynamics of a physiologically structured population in a time-varying environment

Irene Louise Torpe Heilmann, Jens Starke, Ken Haste Andersen, Uffe Høgsbro Thygesen, Mads Peter Sørensen

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Abstract

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.
Original languageEnglish
JournalEcological Complexity
Volume28
Pages (from-to)54-61
ISSN1476-945X
DOIs
Publication statusPublished - 2016

Keywords

  • Structured population model
  • Periodic variation
  • Bifurcation diagram

Cite this

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title = "Dynamics of a physiologically structured population in a time-varying environment",
abstract = "Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.",
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Dynamics of a physiologically structured population in a time-varying environment. / Heilmann, Irene Louise Torpe; Starke, Jens; Andersen, Ken Haste; Thygesen, Uffe Høgsbro; Sørensen, Mads Peter.

In: Ecological Complexity, Vol. 28, 2016, p. 54-61.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Dynamics of a physiologically structured population in a time-varying environment

AU - Heilmann, Irene Louise Torpe

AU - Starke, Jens

AU - Andersen, Ken Haste

AU - Thygesen, Uffe Høgsbro

AU - Sørensen, Mads Peter

PY - 2016

Y1 - 2016

N2 - Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.

AB - Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.

KW - Structured population model

KW - Periodic variation

KW - Bifurcation diagram

U2 - 10.1016/j.ecocom.2016.10.004

DO - 10.1016/j.ecocom.2016.10.004

M3 - Journal article

VL - 28

SP - 54

EP - 61

JO - Ecological Complexity: An International Journal on Biocomplexity in the Environment and Theoretical Ecology

JF - Ecological Complexity: An International Journal on Biocomplexity in the Environment and Theoretical Ecology

SN - 1476-945X

ER -