Question: Finite Topology of a Dynamical System

Help, have no idea what to do.

Obtain a finite topological space from a dynamical system specified as a system of ODEs, by writing Maple code for following steps (use Maple packages DynamicSytems and GraphTheory, preferablly):

  1. Visualize the phase space of the system by plotting solution curves for different initial conditions.

  2. Consider a finite region of the phase space.

  3. Define a finite grid of points in the region.

  4. Define a topology on the grid points based on their connectivity.

  5. Give some useful information regarding the dynamical system in terms of topological properties.

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