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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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A Simple Predator-Prey Population Model with Rich Dynamics
TL;DR: In this article, a non-smooth switched harvest on predators is introduced into a simple predator-prey model with logistical growth of the prey and a bilinear functional response, and it is shown that the system is permanent and there may exist multiple positive equilibria due to the effects of the switched harvest, a saddle-node bifurcation, a limit cycle, and the coexistence of a stable equilibrium and a unstable circled inside limit cycle and a stable circled outside limit cycle.
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Bifurcation from a degenerate simple eigenvalue
TL;DR: In this paper, it was proved that a symmetry-breaking bifurcation occurs at a simple eigenvalue despite the usual transversality condition failing, and this bifurbcation from a degenerate simple Eigenvalue result complements the classical one with the transversal condition.
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An evolutionary game‐theoretic model of cannibalism
TL;DR: It is shown that in the presence of cannibalism, a population can survive under circumstances of low resource availability which, in the absence of cannibalisms, lead to extinction, and that cannibalism can be an evolutionarily stable strategy.
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Integral control for population management.
Christopher Guiver,Hartmut Logemann,Richard Rebarber,Adam Bill,Brigitte Tenhumberg,David J. Hodgson,Stuart Townley +6 more
TL;DR: A novel management methodology for restocking a declining population using integral control, a concept ubiquitous in control theory which has not been applied to population dynamics, is presented.
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Coexistence of competing juvenile-adult structured populations.
TL;DR: A complete account of the global dynamics of the resulting model is given and it is shown that it allows for non-equilibrium competitive coexistence as competition coefficients are increased and occurs in a general class of models for competing populations structured by juvenile and adult life cycle stages.