Differential Equations and Population Dynamics I

<div>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.-&nbsp;Part II Non-Linear Differential and Difference Equations:&nbsp;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.-&nbsp;Part III Applications in Population Dynamics:&nbsp;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.<br></div>