In this work, we analyze the growth of the cumulative number of confirmed infected cases by a novel coronavirus (COVID-19) until March 27, 2020, from countries of Asia, Europe, North America, and South America. Our results show that (i) power-law growth is observed in all countries; (ii) by using the distance correlation, the power-law curves between countries are statistically highly correlated, suggesting the universality of such curves around the world; and (iii) soft quarantine strategies are inefficient to flatten the growth curves. Furthermore, we present a model and strategies that allow the government to reach the flattening of the power-law curves. We found that besides the social distancing of individuals, of well known relevance, the strategy of identifying and isolating infected individuals in a large daily rate can help to flatten the power-laws. These are the essential strategies followed in the Republic of Korea. The high correlation between the power-law curves of different countries strongly indicates that the government containment measures can be applied with success around the whole world. These measures are scathing and to be applied as soon as possible.

This work analyzes the parameter space of a discrete ratchet model and gives direct connections between chaotic domains and a family of isoperiodic stable structures with the ratchet current. The isoperiodic structures, where larger currents are usually observed inside, appear along preferred direction in the parameter space giving a guide to follow the current. Currents in parameter space provide a direct measure of the momentum asymmetry of the multistable and chaotic attractors times the size of the corresponding basin of attraction. Transport structures are shown to exist in the parameter space of the Langevin equation with an external oscillating force.

This work presents numerical evidence that for discrete dynamical systems with one positive Lyapunov exponent the decay of the distance autocorrelation is always related to the Lyapunov exponent. Distinct decay laws for the distance autocorrelation are observed for different systems, namely, exponential decays for the quadratic map, logarithmic for the Hénon map, and power-law for the conservative standard map. In all these cases the decay exponent is close to the positive Lyapunov exponent. For hyperchaotic conservative systems the power-law decay of the distance autocorrelation is not directly related to any Lyapunov exponent.

The nonlinear dynamics of a FitzHugh–Nagumo (FHN) neuron driven by an oscillating current and perturbed by a Gaussian noise signal with different intensities $D$ is investigated. In the noiseless case, stable periodic structures [Arnold tongues (ATS), cuspidal and shrimp-shaped] are identified in the parameter space. The periods of the ATSs obey specific generating and recurrence rules and are organized according to linear Diophantine equations responsible for bifurcation cascades. While for small values of $D$ , noise starts to destroy elongations (“antennas”) of the cuspidals, for larger values of $D$ , the periodic motion expands into chaotic regimes in the parameter space, stabilizing the chaotic motion, and a transient chaotic motion is observed at the periodic-chaotic borderline. Besides giving a detailed description of the neuronal dynamics, the intriguing novel effect observed for larger $D$ values is the generation of a regular dynamics for the driven FHN neuron. This result has a fundamental importance if the complex local dynamics is considered to study the global behavior of the neural networks when parameters are simultaneously varied, and there is the necessity to deal the intrinsic stochastic signal merged into the time series obtained from real experiments. As the FHN model has crucial properties presented by usual neuron models, our results should be helpful in large-scale simulations using complex neuron networks and for applications.