brainmass.sys2nd

brainmass.sys2nd#

brainmass.sys2nd(A, a, u, x, v)[source]#

Compute the acceleration of a second-order linear system.

Implements the canonical second-order kinetic block used by neural-mass models (e.g. Jansen-Rit). The system

\[\frac{d^2 x}{dt^2} + 2 a \frac{dx}{dt} + a^2 x = A\,a\,u\]

is written in state-space form with v = dx/dt as

\[\frac{dv}{dt} = A\,a\,u - 2 a v - a^2 x .\]

Parameters:

A (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Amplitude gain parameter.
a (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Time-constant parameter (units of inverse time).
u (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Input signal.
x (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Position state (the integrated output).
v (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Velocity state (the derivative of x).

Returns:

dv/dt — the acceleration, i.e. the derivative of the velocity state.

Return type: