Cesar Manchein

Universidade do Estado de Santa Catarina, Departamento de Física, Adjunct

Followers

Following

Co-authors

Public Views

Interests

Uploads

Papers by Cesar Manchein

Characterizing the dynamics of three FitzHugh-Nagumo neurons network

Estudo das Propriedades de Caos Fraco em Sistemas Conservativos e Intermitentes

Duas partículas clássicas confinadas num bilhar unidimensional e interagindo via potencial de Yukawa

ABSTRACT

Instability statistics and mixing rates

Physical Review E Statistical Nonlinear and Soft Matter Physics, Jun 3, 2009

We claim that looking at probability distributions of finite time largest Lyapunov exponents, and... more We claim that looking at probability distributions of finite time largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of polynomial decay rates of time correlations and Poincaré recurrences in the-quite-delicate case of dynamical systems with weak chaotic properties.

Download

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-M... more 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 do not have singularities in the marginal fixed point, escape and Poincaré recurrence time statistics that share a power-law decay exponent modified by a clear dimensional scaling, while the rate of phasespace filling and the convergence of ensembles of Lyapunov exponents show a 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.

Download

Quantum-classical transition and quantum activation of ratchet currents in the parameter space

by Marcus Beims and Cesar Manchein

Physical Review E

The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor mod... more The quantum ratchet current is studied in the parameter space of the dissipative kicked rotor model coupled to a zero temperature quantum environment. We show that vacuum fluctuations blur the generic isoperiodic stable structures found in the classical case. Such structures tend to survive when a measure of statistical dependence between the quantum and classical currents are displayed in the parameter space. In addition, we show that quantum fluctuations can be used to overcome transport barriers in the phase space. Related quantum ratchet current activation regions are spotted in the parameter space. Results are discussed {based on quantum, semiclassical and classical calculations. While the semiclassical dynamics involves vacuum fluctuations, the classical map is driven by thermal noise.

Download

ARXIVpreview

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

by Marcus Beims and Cesar Manchein

Physical Review E, 2015

We analyze the recurrence-time statistics (RTS) in three-dimensional non-Hamiltonian volume-prese... more 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.

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

Physica A: Statistical Mechanics and its Applications, 2015

Download

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

by Marcus Beims and Cesar Manchein

Physica A: Statistical Mechanics and its Applications, 2014

Weak chaos in high-dimensional conservative systems can be characterized through sticky effect in... more 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 whole phase space relevant dynamics in 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 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.

Download

Ratchetlike pulse controlling the Fermi deceleration and hyperacceleration

by Marcus Beims and Cesar Manchein

Using an ac driven asymmetric pulse we show how the Fermi acceleration (deceleration) can be cont... more Using an ac driven asymmetric pulse we show how the Fermi acceleration (deceleration) can be controlled. A deformed sawtooth (Ratchetlike) pulse representing the moving wall in the static Fermi-Ulam model is considered. The time integral from the pulse over one period of oscillation must be negative to obtain deceleration and positive to obtain hyperacceleration. We show that while the decelerated case is chaotic, for the hyperaccelerated case the Lyapunov exponents converge to zero. Numerical simulations indicate that the hyperaccelerated case is ergodic in velocity space. Switching between different pulse deformations we are able to control the particle acceleration. Results should be valid for any pulse for which the time integral can be manipulated between positive and negative values.

format_quoteDifferent phase space behaviors emerge from varying asymmetry parameters, affecting the stability and acceleration of particles.format_quote

Download

Energy Redistribution in Higher Dimensions and Chaotic Motion

by Marcus Beims, Cesar Manchein, and Jane Rosa

A system plus environment conservative model is used to charac-terize the nonlinear dynamics when... more A system plus environment conservative model is used to charac-terize the nonlinear dynamics when the time averaged energy for the system particle starts to decay. The system particle dynamics is regular for low values of the N environment oscillators and be-comes chaotic in the interval 13 ≤ N ≤ 15, where the system time averaged energy starts to decay. To characterize the nonlinear mo-tion we estimate the Lyapunov exponent (LE) and determine the power spectrum. For much larger values of N the energy of the system particle is completely transferred to the environment and the corresponding LEs decrease.

Download

Da Complexidade da Natureza à Complexidade da Matemática

Dynamics of two particles interacting in a one dimension billiard

Numerical bifurcation analysis of two coupled FitzHugh-Nagumo oscillators

by Cesar Manchein and Juliana dos Santos

The European Physical Journal B, 2014

The behavior of neurons can be modeled by the FitzHugh-Nagumo oscillator model, consisting of two... more 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 presents multistability shown in the planes of the basin of attractions.

Download

Estudo numérico do mapa padrão dissipativo relativístico

by Cesar Manchein and Ana Horstmann

Bifurcation structures and transient chaos in a four-dimensional Chua model

Physics Letters A, 2014

A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerica... more A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both methods the bifurcation structures of the model were obtained with the possibility to describe the shrimp-shaped domains and their endoskeletons. We study the effect of a parameter that controls the dimension of the system leading the model to present transient chaos with its corresponding basin of attraction being riddled.

Download

Conservative generalized bifurcation diagrams

by Marcus Beims and Cesar Manchein

Physics Letters A, 2013

Bifurcation cascades in conservative systems are shown to exhibit a generalized diagram, which co... more Bifurcation cascades in conservative systems are shown to exhibit a generalized diagram, which contains all relevant informations regarding the location of periodic orbits (resonances), their width (island size), irrational tori and the infinite higher-order resonances, showing the intricate way they are born. Contraction rates for islands sizes, along period-doubling bifurcations, are estimated to be α I ∼ 3.9. Results are demonstrated for the standard map and for the continuous Hénon-Heiles potential. The methods used here are very suitable to find periodic orbits in conservative systems, and to characterize the regular, mixed or chaotic dynamics as the nonlinear parameter is varied.

format_quoteFinite Time Lyapunov Exponent convergence is utilized to map stable orbital points and bifurcation diagrams effectively.format_quote

Download

Ratchet Transport and Periodic Structures in Parameter Space

by Marcus Beims and Cesar Manchein

Physical Review Letters, 2011

Ratchet models are prominent candidates to describe the transport phenomenum in nature in the abs... more Ratchet models are prominent candidates to describe the transport phenomenum in nature in the absence of external bias. 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 appear along preferred direction in the parameter space giving a guide to follow the current, which usually increases inside the structures but is independent of the corresponding period. One of such structures has the shrimp-shaped form which is known to be an universal structure in the parameter space of dissipative systems. 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.

Download

Temperature Resistant Optimal Ratchet Transport

by Marcus Beims and Cesar Manchein

Physical Review Letters, 2013

Stable periodic structures containing optimal ratchet transport, recently found in the parameter ... more Stable periodic structures containing optimal ratchet transport, recently found in the parameter space dissipation versus ratchet parameter [PRL 106, 234101 (2011)], are shown to be resistant to reasonable temperatures, reinforcing the expectation that they are essential to explain the optimal ratchet transport in nature. Critical temperatures for their destruction, valid from the overdamping to close to the conservative limits, are obtained numerically and shown to be connected to the current efficiency, given here analytically. Results are demonstrated for a discrete ratchet model and generalized to the Langevin equation with an additional external oscillating force.

format_quoteIsoperiodic stable structures (ISSs) govern ratchet currents, bounding efficient transport regions and informing the diversity of currents.format_quote

Download

Cesar Manchein

Uploads

Papers by Cesar Manchein

Log In