arXiv subjects

Cesar Manchein

Publications and source records attributed to Cesar Manchein.

At least 19 recordsLinked to original sources

arXiv2024

Lyapunov stability under $q$-dilatation and $q$-contraction of coordinates

This study examines the Lyapunov stability under coordinate $q$-contraction and $q$-dilatation in three dynamical systems: the discrete-time dissipative H\'enon map, and the conservative, non-integrable, continuous-time H\'enon-Heiles and diamagnetic Kepler problems. The stability analysis uses the $q$-deformed Jacobian and $q$-derivative, with trajectory stability assessed for $q > 1$ (dilatation) and $q < 1$ (contraction). Analytical curves in the parameter space mark boundaries of distinct low-periodic motions in the H\'enon map. Numerical simulations compute the maximal Lyapunov exponent across the parameter space, in Poincar\'e surfaces of section, and as a function of total energy in the conservative systems. Simulations show that $q$-contraction ($q$-dilatation) generally decreases (increases) positive Lyapunov exponents relative to the $q = 1$ case, while both transformations tend to increase Lyapunov exponents for regular orbits. Some exceptions to this trend remain unexplained regarding Kolmogorov-Arnold-Moser (KAM) tori stability.

nlin.CD↗

arXiv2023

Records and occupation time statistics for area-preserving maps

A relevant problem in dynamics is to characterize how deterministic systems may exhibit features typically associated to stochastic processes. A widely studied example is the study of (normal or anomalous) transport properties for deterministic systems on a non-compact phase space. We consider here two examples of area-preserving maps: the Chirikov-Taylor standard map and the Casati-Prosen triangle map, and we investigate transport properties, records' statistics and occupation time statistics. While the standard map, when a chaotic sea is present, always reproduces results expected for simple random walks, the triangle map -- whose analysis still displays many elusive points -- behaves in a wildly different way, some of the features being compatible with a transient (non conservative) nature of the dynamics.

nlin.CD↗

arXiv2020

How relevant is the decision of containment measures against COVID-19 applied ahead of time?

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 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.

physics.soc-ph↗

arXiv2020

Strong correlations between power-law growth of COVID-19 in four continents and the inefficiency of soft quarantine strategies

In this work we analyse the growth of the cumulative number of confirmed infected cases by the COVID-19 until March 27th, 2020, from countries of Asia, Europe, North and South America. Our results show (i) that power-law growth is observed for all countries; (ii) by using the distance correlation, that the power-law curves between countries are statistically highly correlated, suggesting the universality of such curves around the World; and (iii) that soft quarantine strategies are inefficient to flatten the growth curves. Furthermore, we present a model and strategies which allow the government to reach the flattening of the power-law curves. We found that, besides the social distance 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 essentially the strategies used in the Republic of Korea. The high correlation between the power-law curves of different countries strongly indicate that the government containment measures can be applied with success around the whole World. These measures must be scathing and applied as soon as possible.

physics.soc-ph↗

arXiv2019

Optimal ratchet current for elastically interacting particles

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, 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.

nlin.CD↗

arXiv2019

Intermittent stickiness synchronization

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 arbitrary 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 to 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 to find 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 SSs become rare events.

nlin.CD↗

arXiv2018

Steering multiattractors to overcome parameter inaccuracy and noise effects

Steering of attractors in multistable systems is used to increase the available parameter domains which lead to stable dynamics in nonlinear physical systems, reducing substantially undesirable effects of parametric inaccuracy and noise. The procedure proposed here uses time and/or space asymmetric perturbations to move independent multistable attractors in phase space. Applying this mechanism we increase around 230% the stable domains in H\'enon's map, roughly 85% in the ratchet current described by the Langevin equation and 60% in Chua's electronic circuit. The proposal is expected to have wide applications in generic nonlinear complex system presenting multistability, so that related experiments can increase robustness under parametric inaccuracy and noise.

nlin.CD↗

arXiv2018

Optimizing thermally affected ratchet currents using periodic perturbations

The purpose of the present work is to apply a recently proposed methodology to enlarge parameter domains for which optimal ratchet currents (RCs) are obtained. This task is performed by adding a suitable periodic perturbation $F_j$ on a Ratchet mapping and the procedure consists in multiplying a particular class of generic Isoperiodic Stable Structures (ISSs), since the existence of non-zero RCs is directly related to the occurrence of stable domains. By proliferating the ISSs, it is possible to: (i) postpone thermal effects that usually increase the chaotic domain and (ii) demonstrate, by using a quantitative analysis, that the area which provides optimal RCs in the two-dimensional parameter space can be enlarged about $78\%$. In addition, for some specific parameter combinations, non-zero RCs can be induced through the birth of a new attractor, which moves away as the strength of $F_j$ increases. Clearly, the methodology applied to the ratchet mapping is an efficient way to deal with unavoidable thermal effects and its consequent undesirable dynamics, specially in experimental setups. As a second general remark, we conclude that our main findings can be extended to issues related to transport problems.

cond-mat.stat-mech↗

arXiv2018

Exploring conservative islands using correlated and uncorrelated noise

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 (LEs) 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.

nlin.CD↗

arXiv2017

Controlling intermediate dynamics in a family of quadratic maps

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.

nlin.CD↗

arXiv2017

Proliferation of stability in phase and parameter spaces of nonlinear systems

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 H\'enon 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.

nlin.CD↗

arXiv2017

The effect of temperature on generic stable periodic structures in the parameter space of dissipative relativistic standard map

In this work, we have characterized changes in the dynamics of a two-dimensional relativistic standard map in the presence of dissipation and specially when it is submitted to thermal effects modeled by a Gaussian noise reservoir. By the addition of thermal noise in the dissipative relativistic standard map (DRSM) it is possible to suppress typical stable periodic structures (SPSs) embedded in the chaotic domains of parameter space for large enough temperature strengths. Smaller SPSs are first affected by thermal effects, starting from their borders, as a function of temperature. To estimate the necessary temperature strength capable to destroy those SPSs we use the largest Lyapunov exponent to obtain the critical temperature ($T_C$) diagrams. For critical temperatures the chaotic behavior takes place with the suppression of periodic motion, although, the temperature strengths considered in this work are not so large to convert the deterministic features of the underlying system into a stochastic ones.

nlin.CD↗

arXiv2016

Anomalous dynamics and the choice of Poincar\'e recurrence-set

We investigate the dependence of Poincar\'e recurrence-times 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 procedure, which is shown to be quite effective in the detection of tiny regions of regular motion, allows to explain it why similar recurrence-sets have very different distributions and how to modify them in order to enhance their return probabilities. Applied on data, this permits to understand the co-existence of extremely long, transient power-like decays whose anomalous exponent depends on the chosen recurrence-set.

nlin.CD↗

arXiv2016

Correlation decay and large deviations for mixed systems

We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.

nlin.CD↗

arXiv2015

Recurrence-time statistics in non-Hamiltonian volume preserving maps and flows

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 before impenetrable regular islands from the uncoupled case. Essentially the plateaus found in the RTS are related to trajectories that stay long times inside trapping tubes, not allowing recurrences, and then penetrates 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 (quasi-regular 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.

nlin.CD↗

arXiv2015

Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two nonlinear differential equations, which simulates the behavior of nerve impulse conduction through the neuronal membrane. In this work, we numerically study the dynamical behavior of two coupled FitzHugh-Nagumo oscillators. We consider unidirectional and bidirectional couplings, for which Lyapunov and isoperiodic diagrams were constructed calculating the Lyapunov exponents and the number of the local maxima of a variable in one period interval of the time-series, respectively. By numerical continuation method the bifurcation curves are also obtained for both couplings. The dynamics of the networks here investigated are presented in terms of the variation between the coupling strength of the oscillators and other parameters of the system. For the network of two oscillators unidirectionally coupled, the results show the existence of Arnold tongues, self-organized sequentially in a branch of a Stern-Brocot tree and by the bifurcation curves it became evident the connection between these Arnold tongues with other periodic structures in Lyapunov diagrams. That system also present multistability shown in the planes of the basin of attractions.

nlin.CD↗

arXiv2014

Extensive numerical investigations on the ergodic properties of two coupled Pomeau-Manneville maps

We present extensive numerical investigations on the ergodic properties of two identical Pomeau-Manneville maps interacting on the unit square through a diffusive linear coupling. The system exhibits anomalous statistics, as expected, but with strong deviations from the single intermittent map: Such differences are characterized by numerical experiments with densities which {\it do not} have singularities in the marginal fixed point, escape and Poincar\'e recurrence time statistics that share a power-law decay exponent modified by a clear {\it dimensional} scaling, while the rate of phase-space filling and the convergence of ensembles of Lyapunov exponents show a {\it stretched} instead of pure exponential behaviour. In spite of the lack of rigorous results about this system, the dependence on both the intermittency and the coupling parameters appears to be smooth, paving the way for further analytical development. We remark that dynamical exponents appear to be independent of the (nonzero) coupling strength.

nlin.CD↗

arXiv2014

Characterizing weak chaos in nonintegrable Hamiltonian systems: the fundamental role of stickiness and initial conditions

Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite time Lyapunov exponents (FTLEs) distribution. They gather the {\it whole} phase space relevant dynamics in {\it one} quantity and give informations about ordered and random states. This is analyzed here for discrete Hamiltonian systems with local and global couplings. It is also shown that FTLEs plotted {\it versus} initial condition (IC) and the nonlinear parameter is essential to understand the fundamental role of ICs in the dynamics of weakly chaotic Hamiltonian systems.

nlin.CD↗