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An introduction to structured population dynamics
TLDR
In this paper, the authors present a case study of multispecies interactions with continuous models of age-structured models and show that these models can be used in a variety of applications.Abstract:
Preface 1 Discrete Models Matrix Models Autonomous Single Species Models Some Applications A Case Study Multispecies Interactions 2 Continuous Models Age-Structured Models Autonomous Age-Structured Models Some Applications Multispecies Interactions Other Structured Models 3 Population Level Dynamics Ergodicity and Nonlinear Models The Linear Chain Trick Hierarchical Models Total Population Size in Age-Structured Models Appendix A Stability Theory for Maps Linear Maps Linearization of Maps Appendix B Bifurcation Theorems A Global Bifurcation Theorem Local Parameterization Appendix C Miscellaneous Proofs Bibliography Indexread more
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Stability conditions for a non-linear size-structured model
TL;DR: In this article, a general non-linear size-structured population dynamical model with size and density-dependent fertility and mortality rates and with size-dependent growth rate is considered.
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A chaotic attractor in ecology: theory and experimental data
Jim M. Cushing,Shandelle M. Henson,Robert A. Desharnais,Brian Dennis,R. F. Costantino,Aaron A. King +5 more
TL;DR: In this article, a deterministic LPA model was used to predict the behavior of a population of flour beetles (Tribolium castaneum) in controlled laboratory experiments, including a specific route to chaos.
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Qualitative Analysis of a Prey-Predator Model with Stage Structure for the Predator
TL;DR: It is found that a Hopf bifurcation occurs in the ODE system, but no Turing pattern happens in the reaction-diffusion system; however, when a natural cross diffusion term is included in the model, it can prove the emergence of stationary patterns for this system.
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Introducing a Population into a Steady Community: The Critical Case, the Center Manifold, and the Direction of Bifurcation
TL;DR: It is argued that population invasion models, regardless of the biology that underlies them, take a specific form that significantly simplifies the center manifold analysis.
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Linear stability and positivity results for a generalized size-structured Daphnia model with inflow§
TL;DR: In this article, the authors employ semigroup and spectral methods to analyze the linear stability of positive stationary solutions of a generalized size-structured Daphnia model, and derive a comprehensive instability criterion that reduces to an elegant instability condition for the classical Daphia population model in terms of the inherent net reproduction rate of Daphania individuals.