Blinking Networks of Memristor Oscillatory Circuits in the Flux-Charge Domain - Lanza, Valentina; Secco, Jacopo; Corinto, Fernando (Frontiers in Neuroscience, 2021)
Multistability phenomena and complex nonlinear dynamics in memristor oscillators pave the way to obtain efficient solutions to optimization problems by means of novel computational architectures (Kumar et al., 2017) based on the interconnection of single– device oscillators. It is well-know that topological properties of interconnections permit to control synchronization and spatio–temporal patterns in oscillatory networks. When the interconnections can change in time with a given probability to connect two oscillators, the whole network acts as a complex network with blinking couplings. The work of Belykh et al (Belykh et al., 2004a) has shown that blinking complex networks are able to completely synchronize faster with respect to other coupling strategies. This work focuses on blinking complex networks made of memristor oscillators. By exploiting the recent Flux– Charge Analysis Method, we make clear that synchronization phenomena in networks of memristor oscillators having stochastic couplings, i.e. Blinking Memristor Oscillatory Networks (BMONs), correspond to global periodic oscillations on invariant manifolds and the effect of a blinking link is to shift the nonlinear dynamics through the infinite (invariant) manifolds. Numerical simulations performed on memristor oscillatory circuits prove that synchronization phenomena can be controlled just by changing the coupling amongst them.