Maple 10 Worksheets for Dynamical Systems

Information about textbook, "Introduction to Dynamical Systems"


Part 1: Systems of Nonlinear Differential Equations
Linear Systems
Linear systems in 2 dimensions: numerical plot
Linear systems in 3 dimensions: numerical plot
Numerical Methods
Numerical solutions for scalar equation: Euler, Improved Euler, Runge-Kutta
Numerical solutions for two dimensional system of equation: Euler, Improved Euler, Runge-Kutta
One dimensional plots
Plot of one dimensional solutions
Two dimensional plots
Phase portrait for nonlinear system in the plane
Phase portrait for competitive system (coexistence)
Phase portrait for Lienard system: contains (t,x)-plot
Three dimensional plots
Phase portrait for Lorenz system
Phase portrait for 3 dimensional system (Rossler system)
Poincare map for the forced duffing equation
Part 2: Iteration of Functions
Iterate the cosine function
Iterate the tent map
Iterate the general tent map with a parmater
Graphical representation of the iterates of the logistic (quadratic) function.
Graph of the n-th iterate of the logistic (quadratic) function.
Hassel model for population
Sensitive dependence on initial conditions
Finding periodic points by Newton's method
Calculating the Lyapunov exponent for f(x) = r*x*(1-x)
Iterates of the beetle population