Rationale behind auto-AUTO

auto-AUTO redefines the notion of branch found in AUTO. A branch in auto-AUTO regroups both a forward and a backward continuations together. A base class Continuation was designed to include shared methods and attributes for the different types (fixed points, periodic orbits, ?). For the moment, there are two main classes of continuations:

• FixedPointContinuation: to perform continuation of fixed points based on initial data or on a AUTOSolution object.

• PeriodicOrbitContinuation: to perform continuation of periodic orbits based on initial data or on a AUTOSolution object.

These two classes form the building blocks used by the classes devoted to the construction of the tree of bifurcation and regime diagrams. For the moment, only bifurcation diagrams are possible, with the class:

• BifurcationDiagram

Regime diagrams class development is planned in the future.

These diagrams classes include the logic to expand and compute the bifurcation tree, and will perform these computations up to pre-specified level.

auto-AUTO has been designed with bifurcations of continuous-time dynamical system in mind. algebraïc and discrete-time systems could work but have not been tested. Homoclinic continuations are out of the scope of auto-AUTO.