Abstract
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 based on the interconnection of single–device oscillators. It is well-known 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 has shown that a particular class of blinking complex networks are able to completely synchronize in a faster fashion with respect to other coupling strategies. This work focuses on the specific class of blinking complex networks made of Memristor–based Oscillatory Circuits (MOCs). By exploiting the recent Flux–Charge Analysis Method, we make clear that synchronization phenomena in blinking 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 MOCs prove that synchronization phenomena can be controlled just by changing the coupling amongst them.
Highlights
Synchronization of complex networks with interacting units is an active research topic with applications in many fields such as engineering, computer sciences, neural networks, neuromorphic circuit computing and information security. Arenas et al (2008) formulated a comprehensive review in 2008, describing the impacts of this field of research
One of the most challenging problem in complex network is the study of spatio–temporal patterns emerging from synchronization phenomena and their relationship with the network topology and interactions’ dynamics among the network units
The ultimate goal of the manuscript is to show that blinking couplings in complex networks of memristor oscillators induce bifurcations without parameters so that the whole dynamics of a Blinking Memristor Oscillatory Networks (BMONs) takes place on an invariant manifold where periodic oscillations correspond to synchronized states. In this manuscript analysis of nonlinear dynamics and numerical simulations are focused on a specific BMON in which each oscillator is a third–order dynamical system describing the Chua’s circuit with a memristor replacing the nonlinear resistor, but the FluxCharge Analysis Method (FCAM) provides the theoretical framework to grasp the role of network topology in BMONs including Memristor–based Oscillator Circuit (MOCs) of any order
Summary
Synchronization of complex networks with interacting units is an active research topic with applications in many fields such as engineering, computer sciences, neural networks (both biological and not), neuromorphic circuit computing and information security. Arenas et al (2008) formulated a comprehensive review in 2008, describing the impacts of this field of research. The ultimate goal of the manuscript is to show that blinking couplings in complex networks of memristor oscillators induce bifurcations without parameters so that the whole dynamics of a BMON takes place on an invariant manifold where periodic oscillations correspond to synchronized states. In this manuscript analysis of nonlinear dynamics and numerical simulations are focused on a specific BMON in which each oscillator is a third–order dynamical system describing the Chua’s circuit with a memristor replacing the nonlinear resistor, but the FCAM provides the theoretical framework to grasp the role of network topology in BMONs including Memristor–based Oscillator Circuit (MOCs) of any order. Synchronization phenomena in BMONs are analyzed via numerical simulations
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