Second 3-week block: project guide

Explore how exact solutions to first order differential equations differ from Euler approximations.
Experiment with Euler approximations to the Lorenz equations for various parameter values and initial conditions.
The Lotka-Volterra predator-prey equations are $\frac{dx}{dt} = x(\alpha - \beta y), \frac{dy}{dt} = - y(\gamma - \delta x)$ where y is the number of predators, x is the number of prey, and $\alpha, \beta, \gamma,\delta$ are parameters that tune the interaction of the predators and prey. Explore solutions of the predator-prey equations for varying parameter values and initial conditions.
Explore the behavior of the Rössler system of differential equations $\frac{dx}{dt} =-y-z, \frac{dy}{dt} =x+ay, \frac{dz}{dt} =b+z(x-c)$ for various parameter values and initial conditions.