chapter  17
30 Pages

Weakly Connected Oscillatory Networks for Information Processing

WithMICHELE BONNIN, FERNANDO CORINTO, ANDMARCO GILLI

Contents 17.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 17.2 Networks of Structurally Stable Oscillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 429 17.3 Networks of Oscillators Close to Bifurcations. . . . . . . . . . . . . . . . . . . . . . . . . . . 434 17.4 Pattern Recognition by Means of Weakly Connected Oscillatory

Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443 17.4.1 WCON-Based Associative Memories . . . . . . . . . . . . . . . . . . . . . . . . . . 446 17.4.2 WCON-Based Dynamic Memories . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

17.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 452 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453

Oscillatory nonlinear networks represent a circuit architecture for image and information processing. In particular, synchronous and/or entrained states can be exploited for dynamic pattern recognition and to realize associative and dynamic memories. In this chapter, we show how the equations governing the dynamical evolution of the network can be recast either to a phase equation, in which each oscillator is only described by its phase, or to an amplitude-phase equation, where each oscillator is described by its amplitude and phase. These models not only represent the ideal frameworks for investigating the emergence of collective behaviors such as synchronous or entrained oscillations but also provide a useful design tool for implementing associative and dynamic memories. The last part of the chapter is devoted to describe this application.