ExternalSystems

ExternalSystem{N_EXT, T, EigenvalueType}

Represents a dynamical system of the form:

dr/dt = f(r) = A r + higher-order terms

where r ∈ ℝ^{N_EXT} (or ℂ^{N_EXT}), A is a constant matrix, and the dynamics are given by a polynomial expansion. The structure stores the full polynomial, the linear matrix, and its eigenvalues.

Fields

• first_order_dynamics::DensePolynomial{T, N_EXT} – the full polynomial dynamics (vector-valued: maps ℂ^{NEXT} → ℂ^{NEXT}).
• linear_matrix::SMatrix{N_EXT, N_EXT, T} – the linear part (Jacobian at the origin).
• eigenvalues::SVector{N_EXT, EigenvalueType} – eigenvalues of the linear matrix. If T<:Real, EigenvalueType = Complex{T}; otherwise EigenvalueType = T.

Constructors

1. ExternalSystem(first_order_dynamics) Build from a polynomial. Computes linear matrix and associated automatically.

2. ExternalSystem(first_order_dynamics, eigenvalues) Same as above, but with precomputed eigenvalues.

3. ExternalSystem(eigenvalues) Construct a purely linear system dx/dt = diag(eigenvalues) * x, i.e., decoupled linear dynamics.