Energy-based theory of autoresonance in chains of coupled damped-driven generic oscillators.

An energy-based theory of autoresonance in driven dissipative chains of coupled generic oscillators is discussed on the basis of a variational principle concerning the energy functional. The theory is applied to chains of delayed Duffing-Ueda oscillators and the equations that together govern the autoresonance forces and solutions are derived and solved analytically for generic values of parameters and initial conditions, including the case of quenched time-delay disorder. Remarkably, the presence of retarded potentials with time-delayed feedback drastically modify the autoresonance scenario preventing the growth of the energy oscillation over specific regions of the parameter space.

Resonancelike emergence of chaos in complex networks of damped-driven nonlinear systems.

Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological networks. Here, we solve a critical outstanding problem in this multidisciplinary research field: the emergence and persistence of spatiotemporal chaos in complex networks of damped-driven nonlinear oscillators in the significant weak-coupling regime, while they exhibit regular behavior when uncoupled. By developing a comprehensive theory with the aid of standard analytical methods, a hierarchy of lower-dimensional effective models, and extensive numerical simulations, we uncover and characterize the basic physical mechanisms concerning both heterogeneity-induced and impulse-induced emergence, enhancement, and suppression of chaos in starlike and scale-free networks of periodically driven, dissipative nonlinear oscillators.

Ratchet universality in coupled dissipative oscillators without external bias.

Directed ratchet transport is generally observed in nonautonomous systems as a result of the interplay of nonlinearity, symmetry breaking, and nonequilibrium fluctuations. Here we demonstrate that ratchet dynamics can appear in significant transporting degrees of freedom of dissipative coupled systems without external bias due to unidirectional coupling of oscillatory degrees of freedom (which are also nonbiasing in any direction), while optimal enhancement of directed ratchet transport occurs when the initial conditions and parameters of such ratcheting degrees of freedom are suitably chosen as predicted by the theory of ratchet universality. The simple case of linear oscillatory degrees of freedom is discussed in detail, and numerical experiments are described which confirm all the theoretical predictions, including the dependence of current (velocity) reversals on the initial conditions and the ratcheting degrees-of-freedom parameters.

Directed ratchet transport of cold atoms and fluxons driven by biharmonic fields: A unified view.

This paper discusses two retrodictions of the theory of ratchet universality which explain previous experimental results concerning directed ratchet transport of cold atoms in dissipative optical lattices in one case and of fluxons in uniform annular Josephson junctions in the other, both driven by biharmonic fields. It has to be emphasized that these retrodictions are in sharp contrast with the current standard explanation of such experimental results, and they offer optimal control of the ratchetlike motion of such entities. New experimental proposals with cold atoms and fluxons are discussed, providing additional tests for novel predictions from ratchet universality.

Identification of minimal parameters for optimal suppression of chaos in dissipative driven systems.

Taming chaos arising from dissipative non-autonomous nonlinear systems by applying additional harmonic excitations is a reliable and widely used procedure nowadays. But the suppressory effectiveness of generic non-harmonic periodic excitations continues to be a significant challenge both to our theoretical understanding and in practical applications. Here we show how the effectiveness of generic suppressory excitations is optimally enhanced when the impulse transmitted by them (time integral over two consecutive zeros) is judiciously controlled in a not obvious way.

Impulse-induced localized control of chaos in starlike networks.

Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e.

Impulse-induced optimum signal amplification in scale-free networks.

Optimizing information transmission across a network is an essential task for controlling and manipulating generic information-processing systems. Here, we show how topological amplification effects in scale-free networks of signaling devices are optimally enhanced when the impulse transmitted by periodic external signals (time integral over two consecutive zeros) is maximum. This is demonstrated theoretically by means of a star-like network of overdamped bistable systems subjected to generic zero-mean periodic signals and confirmed numerically by simulations of scale-free networks of such systems.

Drastic disorder-induced reduction of signal amplification in scale-free networks.

Understanding information transmission across a network is a fundamental task for controlling and manipulating both biological and manmade information-processing systems. Here we show how topological resonant-like amplification effects in scale-free networks of signaling devices are drastically reduced when phase disorder in the external signals is considered. This is demonstrated theoretically by means of a starlike network of overdamped bistable systems, and confirmed numerically by simulations of scale-free networks of such systems.

Reply to "Comment on 'Ratchet universality in the presence of thermal noise' ".

The Comment by Quintero et al. [preceding Comment, Phys. Rev.

Chaotic dynamics of a microswimmer in Poiseuille flow.

The chaotic dynamics of pointlike, spherical particles in cylindrical Poiseuille flow is theoretically characterized and numerically confirmed when their own intrinsic swimming velocity undergoes temporal fluctuations around an average value. Two dimensionless ratios associated with the three significant temporal scales of the problem are identified that fully determine the chaos scenario. In particular, small but finite periodic fluctuations of swimming speed result in chaotic or regular motion depending on the position and orientation of the microswimmer with respect to the flow center line.

Ratchet universality in the presence of thermal noise.

We show that directed ratchet transport of a driven overdamped Brownian particle subjected to a spatially periodic and symmetric potential can be reliably controlled by tailoring a biharmonic temporal force, in coherence with the degree-of-symmetry-breaking mechanism. We demonstrate that the effect of finite temperature on the purely deterministic ratchet scenario can be understood as an effective noise-induced change of the potential barrier which is in turn controlled by the degree-of-symmetry-breaking mechanism. Remarkably, we find that the same universal scenario holds for any symmetric periodic potential, while optimal directed ratchet transport occurs when the impulse transmitted (spatial integral over a half period) by the symmetric spatial force is maximum.

Geometric and colour data fusion for outdoor 3D models.

This paper deals with the generation of accurate, dense and coloured 3D models of outdoor scenarios from scanners. This is a challenging research field in which several problems still remain unsolved. In particular, the process of 3D model creation in outdoor scenes may be inefficient if the scene is digitalized under unsuitable technical (specific scanner on-board camera) and environmental (rain, dampness, changing illumination) conditions.

Breakdown of autoresonance due to separatrix crossing in dissipative systems: From Josephson junctions to the three-wave problem.

Optimal energy amplification via autoresonance in dissipative systems subjected to separatrix crossings is discussed through the universal model of a damped driven pendulum. Analytical expressions of the autoresonance responses and forces as well as the associated adiabatic invariants for the phase space regions separated by the underlying separatrix are derived from the energy-based theory of autoresonance. Additionally, applications to a single Josephson junction, topological solitons in Frenkel-Kontorova chains, as well as to the three-wave problem in dissipative media are discussed in detail from the autoresonance analysis.

Disorder induced control of discrete soliton ratchets.

We demonstrate that directed transport of topological solitons in damped, biharmonically driven Frenkel-Kontorova chains can be strongly enhanced by introducing suitable phase disorder into the asymmetric periodic driving. From a collective coordinate formalism, we theoretically deduce an effective deterministic equation of motion governing the dynamics of the soliton center-of-mass for which we predict the dependence of maximal soliton drift on disorder strength according to recently proposed general scaling laws concerning directed transport induced by symmetry breaking of temporal forces. We find that these results are in excellent agreement with those of computer simulations of the original Frenkel-Kontorova chains.

Controlling chaotic solitons in Frenkel-Kontorova chains by disordered driving forces.

We discuss a general mechanism explaining the taming effect of phase disorder in external forces on chaotic solitons in damped, driven, Frenkel-Kontorova chains. We deduce analytically an effective random equation of motion governing the dynamics of the soliton center of mass for which we obtain numerically the regions in the control parameter space where chaotic solitons are suppressed. We find that such predictions are in excellent agreement with results of computer simulations of the original Frenkel-Kontorova chains.

Controlling the ratchet effect through the symmetries of the systems: application to molecular motors.

We discuss a novel generic mechanism for controlling the ratchet effect through the breaking of relevant symmetries. We review previous works on ratchets where directed transport is induced by the breaking of standard temporal symmetries f(t)=-f(t+T/2) and f(t)=f(-t) (or f(t)=-f(-t)). We find that in seemingly unrelated systems the average velocity (or the current) of particles (or solitons) exhibits common features.

Controlling chaos with localized heterogeneous forces in oscillator chains.

The effects of decreasing the impulse transmitted by localized periodic pulses on the chaotic behavior of homogeneous chains of coupled nonlinear oscillators are studied. It is assumed that when the oscillators are driven synchronously, i.e.

Melnikov method approach to control of homoclinic/heteroclinic chaos by weak harmonic excitations.

A review on the application of Melnikov's method to control homoclinic and heteroclinic chaos in low-dimensional, non-autonomous and dissipative oscillator systems by weak harmonic excitations is presented, including diverse applications, such as chaotic escape from a potential well, chaotic solitons in Frenkel-Kontorova chains and chaotic-charged particles in the field of an electrostatic wave packet.

Taming chaotic solitons in Frenkel-Kontorova chains by weak periodic excitations.

We have proposed theoretically and confirmed numerically the possibility of controlling chaotic solitons in damped, driven Frenkel-Kontorova chains subjected to additive bounded noise by weak periodic excitations. Theoretically, we obtained an effective equation of motion governing the dynamics of the soliton center of mass for which we deduced Melnikov's method-based predictions concerning the regions in the control parameter space where homoclinic bifurcations are frustrated. Numerically, we found that such theoretical predictions can be reliably applied to the original Frenkel-Kontorova chains, even for the case of localized application of the soliton-taming excitations, and there is strikingly good agreement between analytical estimates and numerical results.