This paper provides a global picture of the bifurcation scenario of the Hindmarsh–Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh–Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters.

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.

The presence of synchronized clusters in neuron networks is a hallmark of information transmission and processing. Common approaches to study cluster synchronization in networks of coupled oscillators ground on simplifying assumptions, which often neglect key biological features of neuron networks. Here we propose a general framework to study presence and stability of synchronous clusters in more realistic models of neuron networks, characterized by the presence of delays, different kinds of neurons and synapses. Application of this framework to two examples with different size and features (the directed network of the macaque cerebral cortex and the swim central pattern generator of a mollusc) provides an interpretation key to explain known functional mechanisms emerging from the combination of anatomy and neuron dynamics. The cluster synchronization analysis is carried out also by changing parameters and studying bifurcations. Despite some modeling simplifications in one of the examples, the obtained results are in good agreement with previously reported biological data.

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.