Differential Equations and Population Dynamics I

Arnaud Ducrot is professor of mathematics at the University Le Havre Normandie, France. His research interests include analysis, dynamical systems and mathematical aspects of population dynamics and the natural sciences.Quentin Griette is an associate professor in mathematics at the University of Bordeaux, France. His areas of expertise include ordinary differential equations, reaction-diffusion systems and the numerical computation of their solutions.Zhihua Liu is a professor of mathematics at Beijing Normal University, China. Her research interests include differential equations, dynamical systems and applications in epidemics and population dynamics.Pierre Magal is professor of mathematics at the University of Bordeaux, France. His research interests include differential equations, dynamical systems, numerical simulations and mathematical biology.

• Part I Linear Differential and Difference Equations: 1 Introduction to Linear Population Dynamics.- 2 Existence and Uniqueness of Solutions.- 3 Stability and Instability of Linear.- 4 Positivity and Perron-Frobenius's Theorem.- Part II Non-Linear Differential and Difference Equations: 5 Nonlinear Differential Equation.- 6 Omega and Alpha Limit.- 7 Global Attractors and Uniformly.- 8 Linearized Stability Principle and Hartman-Grobman's Theorem.- 9 Positivity and Invariant Sub-region.- 10 Monotone semiflows.- 11 Logistic Equations with Diffusion.- 12 The Poincare-Bendixson and Monotone Cyclic Feedback Systems.- 13 Bifurcations.- 14 Center Manifold Theory and Center Unstable Manifold Theory.- 15 Normal Form Theory.- Part III Applications in Population Dynamics: 16 A Holling's Predator-prey Model with Handling and Searching Predators.- 17 Hopf Bifurcation for a Holling's Predator-prey Model with Handling and Searching Predators.- 18 Epidemic Models with COVID-19.