Experimental Analysis of Emergent Dynamics in Complex Networks of Nonlinear Oscillators

The aim of this thesis is to explore and investigate the emergent dynamics of complex networks through a novel and insightful experimental setup realized as a configurable network of chaotic Chua's circuits. In particular part of our work has been devoted to the implementation and characterization of a "2.0 hardware version" of it, where the interconnection network has improved greatly in its main features. In this way the setup has been fully automatized in providing control on network structure and coupling strength. A large set of experiments has been carried out in networks with proportional coupling and arbitrary topology, showing, emergent dynamics encompassing synchronization, patterns and traveling waves, clusters formation. Also, the case of dynamic coupling has been experimentally addressed. The experimental observations have been compared with theoretical results by carrying out a local stability analysis of networks with static and dynamic links. Here we use the Master Stability approach (MSF) and its extensions to the case where the links are of dynamic nature (Proportional Derivative-MSF). Last part of the work has been devoted to the experimental study of cluster synchronization, stimulated by novel theoretical advances based on group theory and network symmetries. A novel network structure referred as "Multiplexed Network" has been experimentally examined, resulting in a great enhancement in synchronization, for which no theoretical models are yet available

Experiments on Clustering and Synchronous Patterns in a Configurable Network of Chaotic Oscillators

We present new experimental results on a recently developed set-up, implementing a dynamically configurable network of chaotic oscillators with Chua’s circuits as nodes. The set-up has been designed and tailored to easily perform real time experiments on complex networks with arbitrary topology. We focus here on the emergence of symmetry related synchronization patterns, as well as on the switching among different clusters due to modification of the network structure and/or coupling strength, that are experimentally analyzed for the first time in such type of networks. The observed behavior confirms basic theoretical expectations on small networks, as recently appeared in literature. Moreover the scalability to higher complexity network, as allowed by the considered set-up, is briefly discussed

A didactic electronic set-up for introducing to complex networks of chaotic oscillators

The paper describes a portable didactic experiment, realizing a complex network of Chua's circuits, along with its use for introducing collective dynamics in networks of nonlinear oscillators to students. The equipment enables the full configurability of the node's parameters and the network structure (topology and link impedances). An 8 nodes portable version is realized as a demonstrator, however the corresponding laboratory experiment is designed to be easily scalable to a high number of nodes. The network's control and the data acquisition are automated thanks to a USB interface board and a LabVIEW control interface. The experiment allows the student to perform some direct real time analysis of a set of networked (coupled) Chua's circuits, with the goal to give immediate impact to the discovery of collective behaviors. In particular, the proposed experiences range from the characterization of the complex dynamics of the isolated nodes to the complete synchronization, as well as the emergence of clustering and waves. It is adopted within some course on Advanced Circuit Theory at the Master Degree level

Analogic realization of a non-linear network with re-configurable structure as paradigm for real time analysis of complex dynamics

A novel experimental set-up realized for the real time analysis of reconfigurable complex networks, with chaotic Chua’s circuits as nodes, is considered. It has been designed to easily perform large scale experiments on networks of chaotic oscillators, possibly exploring in real time the parameters space in terms of topologies, coupling strengths, nodes’ dynamics, with potential application in the area of neuro-computing and associative dynamic memories. A sample of the capabilities is given by considering diffusive coupling with a large range of coupling strengths in a set of topologies, and first experiments on a ring of 32 chaotic nodes are reported. Synchronization, chaotic waves and patterns are experimentally observed, and the potential of the realized set-up in terms of accuracy, flexibility and analysis time is fully revealed