This work concerns analytical results on the role of coupling strength in the phenomenon of onset of complete frequency locking in power-grids modelled as a network of second-order Kuramoto oscillators. Those results allow estimation of the coupling strength for the onset of complete frequency locking and to assess the features of network and oscillators that favor synchronization. The analytical results are evaluated using an order parameter defined as the normalized sum of absolute values of phase deviations of the oscillators over time. The investigation of the frequency synchronization within the subsets of the parameter space involved in the synchronization problem is also carried out. It is shown that the analytical results are in good agreement with those observed in the numerical simulations. In order to illustrate the methodology, a case study is presented, involving the Brazilian high-voltage transmission system under a load peak condition to study the effect of load on the syncronizability of the grid. The results show that both the load and the centralized generation might have concurred to the 2014 blackout.

Exploring all its ramifications, we give an overview of the simple yet fundamental bouncing ball problem, which consists of a ball bouncing vertically on a sinusoidally vibrating table under the action of gravity. The dynamics is modeled on the basis of a discrete map of difference equations, which numerically solved fully reveals a rich variety of nonlinear behaviors, encompassing irregular nonperiodic orbits, subharmonic and chaotic motions, chattering mechanisms, and also unbounded nonperiodic orbits. For periodic motions, the corresponding conditions for stability and bifurcation are determined from analytical considerations of a reduced map. Through numerical examples, it is shown that a slight change in the initial conditions makes the ball motion switch from periodic to chaotic orbits bounded by a velocity strip $v=\pm \Gamma ∕(1-\epsilon )$, where $\Gamma$ is the nondimensionalized shaking acceleration and $\epsilon$ the coefficient of restitution which quantifies the amount of energy lost in the ball-table collision.

The recurrence analysis of dynamic systems has been studied since Poincaré’s seminal work. Since then, several approaches have been developed to study recurrence properties in nonlinear dynamical systems. In this work, we study the recently developed entropy of recurrence microstates. We propose a new quantifier, the maximum entropy (${\mathrm{S}}_{\text{max}}$ ). The new concept uses the diversity of microstates of the recurrence plot and is able to set automatically the optimum recurrence neighborhood ($ϵ$ —vicinity), turning the analysis free of the vicinity parameter. In addition, $ϵ$ turns out to be a novel quantifier of dynamical properties itself. We apply ${\mathrm{S}}_{\text{max}}$ and the optimum $ϵ$ to deterministic and stochastic systems. The ${\mathrm{S}}_{\text{max}}$ quantifier has a higher correlation with the Lyapunov exponent and, since it is a parameter-free measure, a more useful recurrence quantifier of time series.

We explore a properly interconnected set of Kuramoto type oscillators that results in a new associative-memory network configuration, which includes second- and third-order additional terms in the Fourier expansion of the network's coupling. Investigation of the response of the network to different external stimuli indicates an increase in the network capability for coding and information retrieval. Comparison of the network output with that of an equivalent experiment with subjects, for recognizing perturbed binary patterns, shows comparable results between the two approaches. We also discuss the enhanced storage capacity of the network.

This paper presents a study of special trajectories attainment for mobile robots based on the dynamical features of chaotic systems. This method of trajectories construction is envisaged for missions for terrain exploration, with the specific purpose of search or patrol, where fast scanning of the robot workspace is required. We propose the imparting of chaotic motion behavior to the mobile robot by means of a planner of goal positions sequence based on an area-preserving chaotic map. As a consequence, the robot trajectories seem highly opportunistic and unpredictable for external observers, and the trajectories's characteristics ensure the quick scanning of the patrolling space. The kinematic modeling and the closed-loop control of the robot are described. The results and discussion of numerical simulations close the paper.