Mathematical Modeling I - preliminary
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740302486
Table of contents: title: Content; title: 1. Introduction; title: 2. Discrete-time models; title: 2.1. Motivation; title: 2.2. An example – bacterial reproduction; title: 2.3. Solution and equilibrium of a discrete model; title: 2.4. Cobwebbing; title: 2.5. General theory and analytical methods; title: 2.6. Optimization of discrete models; title: 3. Continuous-time models; title: 3.1. Motivation and derivation of continuous models; title: 3.2. Differential equation models; title: 3.3. Separation of variables; title: 3.4. Linear equations; title: 3.5. Optimization of continuous models; title: 4. Sensitivity analysis; title: 5. Systems of difference equations (discrete); title: 5.1. Analytical methods; title: 5.2. Some examples; title: 6. Systems of differential equations (continuous); title: 6.1. Some motivation examples; title: 6.2. Nondimensionalization; title: 6.3. Analytical methods; title: 6.4. Higher dimensional systems; title: 7. Bifurcation analysis; title: 7.1. Saddle-node bifurcation; title: 7.2. Transcritical bifurcation; title: 7.3. Pitchfork bifurcation; title: 7.4. Generic saddle-node bifurcation; title: 7.5. Saddle-node, transcritical, and pitchfork bifurcations in two-dimensional systems; title: 7.6. Introduction of Hopf bifurcations; title: 7.7. Normal form of Hopf bifurcation; title: 7.8. Generic Hopf bifurcation; title: 8. Matlab programming; title: 9. Data fitting