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Single-walled carbon nanotubes (SWCNTs) can undergo arbitrarily large nonlinear deformations without permanent damage to the atomic structure and mechanical properties. The dynamic response observed in curved SWCNTs under externally driven forces has fundamental implications in science and technology. Therefore, it is interesting to study the nonlinear dynamics of a damped-driven curved SWCNT oscillator model if two control parameters are varied simultaneously, e.g., the external driven strength and damping parameters. For this purpose, we construct high-resolution two-dimensional stability diagrams and, unexpectedly, we identify (i) the existence of a quint points lattice merged in a domain of periodic dynamics, (ii) the coexistence of different stable states for the same parameter combinations and different initial conditions (multistability), and (iii) the existence of infinite self-organized generic stable periodic structures (SPSs) merged into chaotic dynamics domains. The quint points lattice found here is composed of five distinct stability domains that coalesce and are associated with five different periodic attractors. The multistability is characterized by the coexistence of three different multi-attractors combinations for three exemplary parameter sets: two periodic attractors, two chaotic attractors, or one periodic and one chaotic attractor. This study demonstrates how complex the dynamics of a damped-driven curved SWCNT oscillator model can be when parameters and initial conditions are varied. For this reason, it may have a relevant impact on new theoretical and experimental applications of damped-driven curved SWCNTs.

Assuntos

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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.

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Several dynamical systems in nature can be maintained out-of-equilibrium, either through mutual interaction of particles or by external fields. The particle's transport and the transient dynamics are landmarking of such systems. While single ratchet systems are genuine candidates to describe unbiased transport, we demonstrate here that coupled ratchets exhibit collective transient ratchet transport. Extensive numerical simulations for up to [Formula: see text] elastically interacting ratchets establish the generation of large transient ratchet currents (RCs). The lifetimes of the transient RCs increase with N and decrease with the coupling strength between the ratchets. We demonstrate one peculiar case having a coupling-induced transient RC through the asymmetric destruction of attractors. Results suggest that physical devices built with coupled ratchet systems should present large collective transient transport of particles, whose technological applications are undoubtedly appealing and feasible.

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We analyze the existence of chaotic and regular dynamics, transient chaos phenomenon, and multistability in the parameter space of two electrically interacting FitzHugh-Nagumo (FHN) neurons. By using extensive numerical experiments to investigate the particular organization between periodic and chaotic domains in the parameter space, we obtained three important findings: (i) there are self-organized generic stable periodic structures along specific directions immersed in a chaotic portion of the parameter space; (ii) the existence of transient chaos phenomenon is responsible for long chaotic temporal evolution preceding the asymptotic (periodic) dynamics for particular parametric combinations in the parameter space; and (iii) the existence of various multistable domains in the parameter space with an arbitrary number of attractors. Additionally, we also prove through numerical simulations that chaos, transient chaos, and multistability prevail even for different coupling strengths between identical FHN neurons. It is possible to find multistable attractors in the phase and parameter spaces and to steer them apart by increasing the asymmetry in the coupling force between neurons. Such a strategy can be essential to experimental matters, as setting the right parameter ranges. As the FHN model shares the crucial properties presented by the more realistic Hodgkin-Huxley-like neurons, our results can be extended to high-dimensional coupled neuron models.

Assuntos

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After the spread of COVID-19 out of China, the evolution of the pandemic has shown remarkable similarities and differences between countries around the world. Eventually, such characteristics are also observed between different regions of the same country. Herewith, we introduce a general method that allows us to compare the evolution of the pandemic in different localities inside a large territorial country: in the case of the present study, Brazil. To evaluate our method, we study the heterogeneous spreading of the COVID-19 outbreak until May 30th, 2020, in Brazil and its 27 federative units, which has been seen as the current epicenter of the pandemic in South America. Each one of the federative units may be considered a cluster of interacting people with similar habits and distributed to a highly heterogeneous demographic density over the entire country. Our first set of results regarding the time-series analysis shows that: (i) a power-law growth of the cumulative number of infected people is observed for federative units of the five regions of Brazil; and (ii) the distance correlation calculated between the time series of the most affected federative units and the curve that describes the evolution of the pandemic in Brazil remains about 1 over most of the time, while such quantity calculated for the federative units with a low incidence of newly infected people remains about 0.95. In the second set of results, we focus on the heterogeneous distribution of the confirmed cases and deaths. By applying the epidemiological susceptible-infected-recovered-dead model we estimated the effective reproduction number (ERN) [Formula: see text] during the pandemic evolution and found that: (i) the mean value of [Formula: see text] for the eight most affected federative units in Brazil is about 2; (ii) the current value of [Formula: see text] for Brazil is greater than 1, which indicates that the epidemic peak is far off; and (iii) Ceará was the only federative unit for which the current [Formula: see text]. Based on these findings, we projected the effects of increase or decrease of the ERN and concluded that if the value of [Formula: see text] increases 20%, not only the peak might grow at least 40% but also its occurrence might be anticipated, which hastens the collapse of the public health-care system. In all cases, keeping the ERN 20% below the current value can save thousands of people in the long term.

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The cumulative number of confirmed infected individuals by the new coronavirus outbreak until April 30th, 2020, is presented for the countries: Belgium, Brazil, United Kingdom (UK), and the United States of America (USA). After an initial period with a low incidence of newly infected people, a power-law growth of the number of confirmed cases is observed. For each country, a distinct growth exponent is obtained. For Belgium, UK, and USA, countries with a large number of infected people, after the power-law growth, a distinct behavior is obtained when approaching saturation. Brazil is still in the power-law regime. Such updates of the data and projections corroborate recent results regarding the power-law growth of the virus and their strong Distance Correlation between some countries around the world. Furthermore, we show that act in time is one of the most relevant non-pharmacological weapons that the health organizations have in the battle against the COVID-19, infectious disease caused by the most recently discovered coronavirus. We study how changing the social distance and the number of daily tests to identify infected asymptomatic individuals can interfere in the number of confirmed cases of COVID-19 when applied in three distinct days, namely April 16th (early), April 30th (current), and May 14th (late). Results show that containment actions are necessary to flatten the curves and should be applied as soon as possible.

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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.

Assuntos

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In this work, we show that optimal ratchet currents of two interacting particles are obtained when stable periodic motion is present. By increasing the coupling strength between identical ratchet maps, it is possible to find, for some parametric combinations, current reversals, hyperchaos, multistability, and duplication of the periodic motion in the parameter space. Besides that, by setting a fixed value for the current of one ratchet, it is possible to induce a positive/negative/null current for the whole system in certain domains of the parameter space.

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This work uses the statistical properties of finite-time Lyapunov exponents (FTLEs) to investigate the intermittent stickiness synchronization (ISS) observed in the mixed phase space of high-dimensional Hamiltonian systems. Full stickiness synchronization (SS) occurs when all FTLEs from a chaotic trajectory tend to zero for arbitrarily long time windows. This behavior is a consequence of the sticky motion close to regular structures which live in the high-dimensional phase space and affects all unstable directions proportionally by the same amount, generating a kind of collective motion. Partial SS occurs when at least one FTLE approaches zero. Thus, distinct degrees of partial SS may occur, depending on the values of nonlinearity and coupling parameters, on the dimension of the phase space, and on the number of positive FTLEs. Through filtering procedures used to precisely characterize the sticky motion, we are able to compute the algebraic decay exponents of the ISS and to obtain remarkable evidence about the existence of a universal behavior related to the decay of time correlations encoded in such exponents. In addition we show that even though the probability of finding full SS is small compared to partial SSs, the full SS may appear for very long times due to the slow algebraic decay of time correlations in mixed phase space. In this sense, observations of very late intermittence between chaotic motion and full SS become rare events.

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In this work, noise is used to analyze the penetration of regular islands in conservative dynamical systems. For this purpose we use the standard map choosing nonlinearity parameters for which a mixed phase space is present. The random variable which simulates noise assumes three distributions, namely equally distributed, normal or Gaussian, and power law (obtained from the same standard map but for other parameters). To investigate the penetration process and explore distinct dynamical behaviors which may occur, we use recurrence time statistics (RTS), Lyapunov exponents and the occupation rate of the phase space. Our main findings are as follows: (i) the standard deviations of the distributions are the most relevant quantity to induce the penetration; (ii) the penetration of islands induce power-law decays in the RTS as a consequence of enhanced trapping; (iii) for the power-law correlated noise an algebraic decay of the RTS is observed, even though sticky motion is absent; and (iv) although strong noise intensities induce an ergodic-like behavior with exponential decays of RTS, the largest Lyapunov exponent is reminiscent of the regular islands.

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The intermediate dynamics of composed one-dimensional maps is used to multiply attractors in phase space and create multiple independent bifurcation diagrams which can split apart. Results are shown for the composition of k-paradigmatic quadratic maps with distinct values of parameters generating k-independent bifurcation diagrams with corresponding k orbital points. For specific conditions, the basic mechanism for creating the shifted diagrams is the prohibition of period doubling bifurcations transformed in saddle-node bifurcations.

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In this work, we show how the composition of maps allows us to multiply, enlarge, and move stable domains in phase and parameter spaces of discrete nonlinear systems. Using Hénon maps with distinct parameters, we generate many identical copies of isoperiodic stable structures (ISSs) in the parameter space and attractors in phase space. The equivalence of the identical ISSs is checked by the largest Lyapunov exponent analysis, and the multiplied basins of attraction become riddled. Our proliferation procedure should be applicable to any two-dimensional nonlinear system.

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We investigate the dependence of Poincaré recurrence-time statistics on the choice of recurrence set by sampling the dynamics of two- and four-dimensional Hamiltonian maps. We derive a method that allows us to visualize the direct relation between the shape of a recurrence set and the values of its return probability distribution in arbitrary phase-space dimensions. Such a procedure, which is shown to be quite effective in the detection of tiny regions of regular motion, allows us to explain why similar recurrence sets have very different distributions and how to modify them in order to enhance their return probabilities. Applied to data, this enables us to understand the coexistence of extremely long, transient powerlike decays whose anomalous exponent depends on the chosen recurrence set.

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We analyze the recurrence-time statistics (RTS) in three-dimensional non-Hamiltonian volume-preserving systems (VPS): an extended standard map and a fluid model. The extended map is a standard map weakly coupled to an extra dimension which contains a deterministic regular, mixed (regular and chaotic), or chaotic motion. The extra dimension strongly enhances the trapping times inducing plateaus and distinct algebraic and exponential decays in the RTS plots. The combined analysis of the RTS with the classification of ordered and chaotic regimes and scaling properties allows us to describe the intricate way trajectories penetrate the previously impenetrable regular islands from the uncoupled case. Essentially the plateaus found in the RTS are related to trajectories that stay for long times inside trapping tubes, not allowing recurrences, and then penetrate diffusively the islands (from the uncoupled case) by a diffusive motion along such tubes in the extra dimension. All asymptotic exponential decays for the RTS are related to an ordered regime (quasiregular motion), and a mixing dynamics is conjectured for the model. These results are compared to the RTS of the standard map with dissipation or noise, showing the peculiarities obtained by using three-dimensional VPS. We also analyze the RTS for a fluid model and show remarkable similarities to the RTS in the extended standard map problem.

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The phase space dynamics of higher dimensional nonintegrable conservative systems is characterized via the effect of "sticky" motion on the finite time Lyapunov exponents (FTLEs) distribution. Since a chaotic trajectory suffers the sticky effect when chaotic motion is mixed to the regular one, it offers a way to separate the mixed from the totally chaotic regimes. To detect stickiness, four different measures are used, related to the distributions of the positive FTLEs, and provide conditions to characterize the dynamics. Conservative maps are systematically studied from the uncoupled two-dimensional case up to coupled maps of dimension 20. Sticky motion is detected in all unstable directions above a threshold K(d) of the nonlinearity parameter K for the high dimensional cases d = 10, 20. Moreover, as K increases we can clearly identify the transition from mixed to totally chaotic motion which occurs simultaneously in all unstable directions. Results show that all four statistical measures sensitively characterize the motion in high dimensional systems.