pyeeg.simulate.CTRNN

class pyeeg.simulate.CTRNN(N, W, input_dim=1, output_dim=1, dt=0.001, seed=42, nonlinearity=<function sigmoid>, theta=None, tau=1.0, solver='euler', x0=None)

Continuous Time Recurrent Neural Network (CTRNN) model.

The state \(x\) of the network evolves according to

\[\tau \dot{x} = -x + W o + I\]

where \(o = f(x + \theta)\) is the output of the network through the nonlinearity \(f\), \(I\) is the external input projected through a (trainable) input matrix, and \(\theta\) is a bias term. A (trainable) readout matrix projects the node outputs to the desired output dimension, rescaled into the range [-1, 1] when the nonlinearity is a sigmoid.

Parameters:

  • N (int) – The number of neurons/nodes.

  • W (array_like) – The connectivity matrix. Shape (N, N).

  • input_dim (int) – The dimension of the external input. The input is projected through a zero-initialised matrix of shape (N, input_dim).

  • output_dim (int) – The dimension of the readout. The node outputs are projected through a zero-initialised matrix of shape (output_dim, N).

  • dt (float) – The integration time step in seconds.

  • seed (int) – The random seed used to initialise the network’s random number generator.

  • nonlinearity (callable) – The nonlinearity function applied to the network state. Default is sigmoid (e.g. can use np.tanh()).

  • theta (array_like, optional) – The bias term. Shape (N,). If None, a zero bias is used.

  • tau (float or array_like) – The leaky-integrator time constant \(\tau\) in seconds. A scalar applies to all neurons, an array must have shape (N,). Defaults to 1.

  • solver (str or callable) – Integration scheme used by step(): "euler" (explicit Euler, the default), "euler-maruyama" or "em" (aliases of "euler": with noise the scheme is Euler-Maruyama), "rk4" (classical fourth-order Runge-Kutta), or a custom callable stepper f(derivative, x, dt, *args) -> x_new.

  • x0 (array_like, optional) – The initial state. Shape (N,). If None, the state starts at zero. The output o is initialised consistently with the state.

Raises:

ValueError – If tau is not positive or does not have shape () or (N,), if solver is not a supported name, or if x0 does not have shape (N,).

Methods

CTRNN.read_out()

Compute the readout of the network.

CTRNN.reset()

Reset the network to its initial state.

CTRNN.simulate([x0, tmax, noise, I])

Simulate the CTRNN model and monitor the output.

CTRNN.step([I, noise])

Compute one step of the CTRNN model (the configured solver).