Nonlinear Dynamics and Computing in Recurrent Neural Networks

Nonlinearity is a key concept in the design and implementation of photonic neural networks for computing. This chapter introduces the fundamental models and concepts of recurrent neural networks, with a particular focus on their nonlinear dynamics. We review several types of nonlinear dynamics that emerge in symmetrically connected recurrent neural networks, in which the energy function plays a crucial role. In addition, we introduce the concepts of reservoir computing, covering fundamental models and physical reservoir computing. Overall, this chapter provides a foundation for the theoretical aspects in the subsequent chapters of this book, which explore a variety of photonic neural networks with nonlinear spatiotemporal dynamics.