FreeEnergyMachine

Checkpoint structure to store system state during simulation.

A mutable struct representing a simulated bifurcation system. T: Type parameter for numerical values KIND: Type of bifurcation (:aSB, :bSB, or :dSB)

State of the simulated bifurcation system. x: Position variables p: Momentum variables

Calculate forces for asymmetric simulated bifurcation (aSB). F = -(x^3 + ax) + c0 Σ(Jij xj)

Calculate kinetic energy: K = Σ(p^2/2)

Calculate potential energy for asymmetric simulated bifurcation (aSB). V = Σ(x^4/4 + ax^2/2) - c0 Σ(Jij xi xj)

Calculate potential energy for symmetric simulated bifurcation (bSB). V = Σ(ax^2/2) - c0 Σ(Jij xi xj)

Calculate potential energy for discrete simulated bifurcation (dSB). V = Σ(ax^2/2) - c0 Σ(Jij (xi sign(xj) + xj sign(xi)))

Simulate the bifurcation system using Störmer-Verlet integrator.

Parameters:

• state: Initial state of the system
• sys: Bifurcation system
• nsteps: Number of simulation steps
• dt: Time step size
• a0: Initial control parameter value (default: 1.0)
• a1: Final control parameter value (default: 0.0)
• checkpoint_steps: Number of steps between checkpoints (default: typemax(Int))

Returns:

• Updated state
• Vector of checkpoints