Roadmap for LotkaVolterra.jl

[gajomi]

This issue outlines a roadmap leading to a production version of the LotkaVolterra package. The goals of this package can be separated into three different kinds of functionality

• providing container types to parameterize different kinds of Lotka-Volterra systems
• providing high performance simulation of initial value problems for Lotka-Volterra systems
• analysis of features of different kinds of Lotka-Volterra systems

Within each of these issues there is the need to establish a an api for the basic types and methods.

Associated with these three general kinds of functionality are a number of specific targets that advance the cause of the package

1. Standard Lotka-Volterra predator prey type
   • define type in terms of standard parameters and basic methods
   • symplectic integration of trajectories
   • qualitative behavior methods
   • cycle family type (container type for cycles; seems to be needed)
2. Generalized Lotka-Volterra type
   • define type in terms of standard parameters and basic methods
   • qualitative behavior methods (existence/values of fixed points, cycles and their stabilities)
   • example implementation of parameterized types, like food webs or food chains
3. Generalized Lotka-Volterra predator prey type
   • define type in terms of standard parameters and basic methods
   • implementation of qualitative behavior functions
4. Specialized numerical integration functions
5. Stabilization of the extent of the api for analysis of feature of dynamical systems in the LV context