  We investigate a recurrent neural network model with common external and bias
inputs that can retrieve branching sequences. Retrieval of memory sequences is
one of the most important functions of the brain. A lot of research has been
done on neural networks that process memory sequences. Most of it has focused
on fixed memory sequences. However, many animals can remember and recall
branching sequences. Therefore, we propose an associative memory model that can
retrieve branching sequences. Our model has bias input and common external
input. Kawamura and Okada reported that common external input enables
sequential memory retrieval in an associative memory model with auto- and weak
cross-correlation connections. We show that retrieval processes along branching
sequences are controllable with both the bias input and the common external
input. To analyze the behaviors of our model, we derived the macroscopic
dynamical description as a probability density function. The results obtained
by our theory agree with those obtained by computer simulations.
