## Modeling dynamical systems with recurrent neural networksUniversity of California, San Diego, Department of Computer Science & Engineering, 1994 - Computers - 232 pages |

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### Contents

Background and Related Work | 7 |

Modeling the lobster gastric mill circuit | 29 |

Hopf Bifurcation and HopfHopping during Recurrent Learning | 42 |

4 other sections not shown

### Common terms and phrases

activation function analysis approximation ARTISTE asymptotic backpropagation behavior biological BPTT center manifold chapter complex computation connected converge Cottrell curve derived desired trajectory differential equations discrete network discuss dynamical systems eigenvalues embedding error gradient example feedforward network Figure finite difference framework gap junctions gastric mill GM circuit gradient descent Hopf bifurcation Hopf-hopping Hopfield input INT1 iterated prediction network layer learned oscillation learning rate limit sets linear method network learns network trained neuromodulator neuron nonlinear nullclines orbit oscillation output parameter periodic attractors phase plane phase relationship phase space phase space reconstruction phase-space learning Pol oscillator possible prediction training reciprocal inhibition recurrent hidden units recurrent nets recurrent network recurrent neural networks recurrent training RTRL algorithm self-recurrent sigmoidal units simulations sine waves stable fixed point stable limit cycle subnetworks synapses tasks teacher forcing teacher signals train the network training set Tsung two-unit network values vector field visible units waveform weights