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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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An Integral Collocation Approach Based on Legendre Polynomials for Solving Riccati, Logistic and Delay Differential Equations
TL;DR: In this article, the authors proposed and analyzed some schemes of the integral collocation formulation based on Legendre polynomials, and implemented these formulae to solve numerically======Riccati, Logistic and delay differential equations with variable coefficients.
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Robust set-point regulation for ecological models with multiple management goals.
TL;DR: It is shown that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements, which applies more generally to linear control systems with positive state variables, including a class of infinite-dimensional systems, and thus have broader appeal.
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Asymptotic Behavior and Numerical Simulations for an Infection Load-Structured Epidemiological Model: Application to the Transmission of Prion Pathologies
Antoine Perasso,Ulrich Razafison +1 more
TL;DR: An infection load-structured SI model with exponential growth of the infection, that incorporates a potential external source of contamination, is studies, performing the analysis of the time asymptotic behavior of the solution by exhibiting epidemiological thresholds that ensure extinction or persistence of the disease in the contagion process.
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A center manifold for second order semilinear differential equations on the real line and applications to the existence of wave trains for the Gurtin–McCamy equation
Arnaud Ducrot,Pierre Magal +1 more
TL;DR: In this paper, a smooth center manifold for a rather general class of abstract second-order semi-linear differential equations involving non-densely defined operators was constructed and a suitable fixed point formulation for the graph of the local center manifold was derived to conclude the existence and smoothness of such a local invariant manifold.
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On Nonlinear Age- and Stage-Structured Population Models
TL;DR: In this paper, the authors present and discuss various aspects of discrete nonlinear age and stage-structured population models, and show that such models cover species which exhibit a wide range of different life histories and that one may use them in order to deduce fairly general ecological principles with respect to stability and dynamical outcomes.