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Complex patterns are commonly retrieved in spatially-extended systems formed by coupled nonlinear dynamical units. In particular, Turing patterns have been extensively studied investigating mathematical models pertaining to different fields, such as chemistry, physics, biology, mechanics, and electronics. In this paper, we focus on the emergence of Turing patterns in memristive cellular nonlinear networks by means of spatial pinning control. The circuit architecture is made by coupled units formed by only two elements, namely, a capacitor and a memristor. The analytical conditions for which Turing patterns can be derived in the proposed architecture are discussed in order to suitably design the circuit parameters. In particular, we derive the conditions on the density of the controlled nodes for which a Turing pattern is globally generated. Finally, it is worth to note that the proposed architecture can be considered as the simplest ideal electronic circuit able to undergo Turing instability and give rise to pattern formation.

In this paper, we study synchronization in time-varying networks inherited by the Vicsek's model of self-propelled particles. In our model, each particle/agent moves in a two dimensional space according to the Vicsek's rules and is associated to a chaotic system. The dynamics of two oscillators are coupled with each other only when agents are at a distance less than an interaction radius. We investigate the system behavior with respect to some fundamental parameters, and, in particular, to the noise level, which for increasing intensity drives the system from an ordered motion to a disordered one. We show that the global dynamics is ruled by the interplay between motion characteristics and dynamical coupling with synchronization either favored or inhibited by a coordinated motion of the self-propelled particles. Finally, we provide semi-analytical estimation for the synchronization thresholds for interconnections occurring at a time-scale shorter than that of the associated dynamical systems.

In this work, we experimentally investigate the robustness to noise of synchronization in all the four-nodes network motifs. The experimental setup consists of four Chua's circuits diffusively coupled in order to implement the six different undirected network motifs that can be obtained with four nodes. In this experimental setup, synchronization in the presence of noise injected in one of the network nodes is investigated and network motifs are compared in terms of the synchronization error obtained. The analysis has been then extended to some selected case studies of networks with five and six nodes. Numerical simulations have been also performed and results in agreement with experiments have been obtained. A correlation between node degree and robustness to noise has been found also in these networks.

Memristors are gaining increasing attention as next generation electronic devices. They are also becoming commonly used as fundamental blocks for building chaotic circuits, although often arbitrary (typically piece-wise linear or cubic) flux-charge characteristics are assumed. In this paper, a chaotic circuit based on the mathematical realistic model of the HP memristor is introduced. The circuit makes use of two HP memristors in antiparallel. Numerical results showing some of the chaotic attractors generated by this circuit and the behavior with respect to changes in its component values are described.

In this paper, chaos is applied to the control of moving robots in order to generate random-like trajectories needed in tasks such as exploration, scanning natural terrains or mapping of unknown environments. Synchronization between the robots of a team is achieved by exploiting the paradigm of mirror neurons, i.e. a neural structure playing a key role in the process of imitation and behaviour understanding. The experimental results discussed in the paper demonstrate that the introduced approach can be successfully applied to implement an efficient learning system for mobile robots.

In this paper using a negative feedback scheme we study the problem of synchronizing two systems (each of them made of n independent chaotic circuits) through the transmission of a unique signal (i.e. a scalar variable). To find the appropriate values of the feedback gains, an approach based on the design of an asymptotic observer leading to a set of linear matrix inequalities is used for piecewise linear systems, while for systems with continuous nonlinearities a master stability function approach is adopted. Numerical results showing the suitability of the approach are reported. Furthermore, the experiment showing separation and synchronization of two pairs of chaotic circuits is discussed. Despite the presence of parameter mismatches, separation and synchronization of the two systems can be achieved. This is an experimental demonstration of the successful possibility of multiplexing two (or more) chaotic signals in the same channel.

In this paper the dynamical network model of the interactions within a group of mobile robots is investigated and proposed as a possible strategy for controlling the robots without central coordination. Motivated by the results of the analysis of our simple model, we show that the system performance in the presence of noise can be improved by including long-range connections between the robots. Finally, a suitable strategy based on this model to control exploration and transport is introduced.