Mattia Frasca

Intra-layer synchronization in multiplex networks

We study synchronization of

Autowaves in a Lattice of Memristor-Based Cells

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Chaos control in a chaotic system with only one stable equilibrium point

oscillators indirectly coupled through a medium which is inhomogeneous and has its own dynamics. The system is formalized in terms of a multilayer network, where the top layer is made of disconnected oscillators and the bottom one, modeling the medium, consists of oscillators coupled according to a given topology. The different dynamics of the medium and the top layer is accounted by including a frequency mismatch between them. We show a novel regime of synchronization as intra-layer coherence does not necessarily require inter-layer coherence. This regime appears under mild conditions on the bottom layer: arbitrary topologies may be considered, provided that they support synchronization of the oscillators of the medium. The existence of a density-dependent threshold as in quorum-sensing phenomena is also demonstrated.Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer undergoes a synchronous evolution with all its replicas in other layers, irrespective of whether or not it is synchronized with the other units of the same layer. We analytically derive the necessary conditions for the existence and stability of inter-layer synchronization, and verify numerically the analytical predictions in several cases where such a state emerges. We inspect the impact of the layer topology on the robustness of such a state against a progressive de-multiplexing of the network. Finally, we provide experimental evidence by means of multiplexes of nonlinear electronic circuits, showing the stability of the synchronized manifold despite the intrinsic noise and parameter mismatch in the experiment.

A Concise Guide to Chaotic Electronic Circuits

In this Chapter, a Cellular Neural/Nonlinear Network (CNN) made of memristor-based cells is introduced. The Memristive CNN consists of identical cells, each containing a memristor, an inductor and a capacitor. We show how the Memristive CNN is able to generate autowaves. We investigate then an FPGA-based implementation of it and related experimental results confirming the capabilities of the system to generate autowaves. This shows that memristor can be used not only as a fundamental block of new chaotic circuits, but also to build complex systems made of interacting memristor-based elementary cells. In such systems many complex phenomena may take place like the autowave propagation discussed in this Chapter and thus feasible hardware emulators allowing an experimental investigation of systems based on electrical analogues of memristor devices are required. In this Chapter such a platform has been realized by using an FPGA-based approach which also has the further advantage of being flexible and easily adaptable to the study of other memristor-based complex systems.

Control of Imperfect Nonlinear Electromechanical Large Scale Systems: From Dynamics to Hardware Implementation

The recent finding on the effect of a small bias in Sprott-like systems, i.e., the stabilization of the unstable equilibrium point through the addition of a small bias [1], paves the way to efficient methods for chaos control in such systems. In this work, we investigate the control of one of such systems both in the ideal case of absence of noise and in the presence of noise. We then propose an experimental setup for the experimental verification of the introduced method.