Differential Equations for ecologists
Prerequisites
1
Introduction
1.1
What is this documemt for?
1.2
What is covered?
2
Brief history of dynamical systems theory
2.1
Early development
2.1.1
Limit concept
2.1.2
Using geometry
2.1.3
Chaos
2.1.4
Foliation
2.1.5
Ref - Math
2.2
Ref - Ecology
2.3
Choose your computational tools
2.3.1
R
2.3.2
ODE with
desolve
3
Mathematical prerequisites
3.1
Notations
3.1.1
Sets
3.1.2
Matrices
3.2
Equations
3.2.1
Order 2
3.3
Change of the basis
3.4
Eigen value
3.4.1
Trick in 2 D
3.4.2
Ressources
4
Continuous ODE in one dimension
4.1
General terminology
4.2
Linear case
4.3
Study case
4.3.1
Expanding the equation
5
ODE in multi-dimensions
5.1
Terminology
5.2
Linear system
5.2.1
General case
5.2.2
Trivial case
5.2.3
Diagonalizations
5.2.4
Graphical examples
5.3
Non-Linear systems
5.3.1
Finding the eigen values
5.4
Examples
5.4.1
Lotka Volterra
5.4.2
Rozenzweig-McArthur model
6
About Chaos
References
Published with bookdown on
Differential Equations for ecologists
Chapter 6
About Chaos