Cluster synchronization in networks of coupled oscillators is the subject of broad interest from the scientific community, with applications ranging from neural to social and animal networks and technological systems. Most of these networks are directed, with flows of information or energy that propagate unidirectionally from given nodes to other nodes. Nevertheless, most of the work on cluster synchronization has focused on undirected networks. Here we characterize cluster synchronization in general directed networks. Our first observation is that, in directed networks, a cluster A of nodes might be one-way dependent on another cluster B: in this case, A may remain synchronized provided that B is stable, but the opposite does not hold. The main contribution of this paper is a method to transform the cluster stability problem in an irreducible form. In this way, we decompose the original problem into subproblems of the lowest dimension, which allows us to immediately detect inter-dependencies among clusters. We apply our analysis to two examples of interest, a human network of violin players executing a musical piece for which directed interactions may be either activated or deactivated by the musicians, and a multilayer neural network with directed layer-to-layer connections.

This paper is concerned with modeling of smart textiles, aimed at compensating their intrinsic nonlinearities. In particular, a new model is proposed to compensate for hysteresis and relaxation in strain sensors made of Electrolycra. These sensors are increasingly employed in emerging areas such as wearable electronics and soft robotics for their simple transduction mechanism and low cost. However, being intrinsically nonlinear, the signals measured from these devices need some processing, in order to increase their sensing accuracy. Here, we propose a new model for the compensation of the main distortions intrinsic to these soft sensors, which are mainly caused by hysteresis and relaxation, whose combined effect produces rate-dependent hysteresis. The model capabilities are tested on experimental data measured on Electrolycra. The comparisons with the results obtained with two different models witness the good behavior of the proposed model.

This article is concerned with the design of synthetic central pattern generators (CPGs). Biological CPGs are neural circuits that determine a variety of rhythmic activities, including locomotion, in animals. A synthetic CPG is a network of dynamical elements (here called cells) properly coupled by various synapses to emulate rhythms produced by a biological CPG. We focus on CPGs for locomotion of quadrupeds and present our design approach, based on the principles of nonlinear dynamics, bifurcation theory, and parameter optimization. This approach lets us design the synthetic CPG with a set of desired rhythms and switch between them as the parameter representing the control actions from the brain is varied. The developed four-cell CPG can produce four distinct gaits: walk, trot, gallop, and bound, similar to the mouse locomotion. The robustness and adaptability of the network design principles are verified using different cell and synapse models.

Summary: Switch‐mode power supplies (SMPSs) are widely exploited to interface electrical energy sources to motors and other electrical loads. Inductors are usually the biggest and heaviest components in SMPSs, limiting their overall power density. Therefore, there is an increasing interest in designing SMPSs with partially saturating inductors, because this significantly reduces their weight and size, thus increasing power density. This paper provides a review of nonlinear behavioral models (based on easy‐to‐measure quantities) of the inductance, power loss, and temperature rise of inductors working, at least partially, in magnetic saturation. This survey discusses the pros, cons, and ranges of validity of these models, with a glimpse at their application to SMPS simulation, design, monitoring, and control.

This paper proposes a new modeling approach for ferrite-core (FC) power inductors used in switch-mode power supplies (SMPSs). In particular, a novel power-loss-dependent inductance behavioral model is proposed, whose parameters can be identified through a limited set of proper experimental measurements of inductor current and voltage. Unlike conventional thermal modeling approaches, which require information on core temperature, the proposed behavioral model relies only on easily measurable quantities. The model is also suitable for being implemented in circuit simulators. By comparing PSIM simulations and experimental measurements on a buck converter for commercial FC inductors, we show that the model allows a reliable prediction of the steady-state inductor current, under different SMPS working conditions.

Synchronization of coupled oscillators is a fundamental process in both natural and artificial networks. While much work has investigated the asymptotic stability of the synchronous solution, the fundamental question of the transient behavior toward synchronization has received far less attention. In this work, we present the transverse reactivity as a metric to quantify the instantaneous rate of growth or decay of desynchronizing perturbations. We first use the transverse reactivity to design a coupling-efficient and energy-efficient synchronization strategy that involves varying the coupling strength dynamically according to the current state of the system. We find that our synchronization strategy is able to synchronize networks in both simulation and experiment over a significantly larger (often by orders of magnitude) range of coupling strengths than is possible when the coupling strength is constant. Then, we characterize the effects of network topology on the transient dynamics towards synchronization by introducing the concept of network syncreactivity: A network with a larger syncreactivity has a larger transverse reactivity at every point on the synchronization manifold, independent of the oscillator dynamics. We classify real-world examples of complex networks in terms of their syncreactivity.