Periodic driving shape controls energy transmission.

In the early 2000s, Geniet and Leon [Phys. Rev. Lett.

Supratransmission phenomenon in a Fermi-Pasta-Ulam diatomic lattice.

The nonlinear supratransmission phenomenon in a Fermi-Pasta-Ulam (FPU) diatomic lattice with two forbidden bands is investigated. Using a decoupling ansatz for the motion of the two different sublattices combined with the continuum (quasidiscrete) approximation, we derived analytically the threshold amplitudes of supratransmission occurrence when a sinusoidal driving with frequency in the upper forbidden band (lower forbidden band gap between acoustic and optical modes) is applied at one end. The resulting estimate of the threshold of a lattice with a first heavy particle is different to the one obtained from a lattice with a first light particle, showing the influence of the driven particle and giving also the possibility to have two thresholds on each forbidden gap of a diatomic lattice by switching the order of light (m) and heavy (M) masses.

Diversity-enhanced stability.

We give compelling evidence that diversity, represented by a quenched disorder, can produce a resonant collective transition between two unsteady states in a network of coupled oscillators. The stability of a metastable state is optimized and the mean first-passage time maximized at an intermediate value of diversity. This finding shows that a system can benefit from inherent heterogeneity by allowing it to maximize the transition time from one state to another at the appropriate degree of heterogeneity.

Enhanced signal response in globally coupled networks of bistable oscillators: Effects of mean field density and signal shape.

This paper studies a set of globally coupled bistable oscillators, all subjected to the same weak periodic signal and identical coupling. The effect of mean field density (MFD) on global dynamics is analyzed. The oscillators switch from intra- to interwell motion as MFD increases, clearly demonstrating MFD-enhanced signal amplification.

Using coupling imperfection to control amplitude death.

Previous studies of nonlinear oscillator networks have shown that amplitude death (AD) occurs after tuning oscillator parameters and coupling properties. Here, we identify regimes where the opposite occurs and show that a local defect (or impurity) in network connectivity leads to AD suppression in situations where identically coupled oscillators cannot. The critical impurity strength value leading to oscillation restoration is an explicit function of network size and system parameters.

Collective escape and supratransmission phenomena in a nonlinear oscillators chain.

In this study, the collective escape and supratransmission phenomena along a nonlinear chain of coupled particles subjected to a cubic on-site potential are considered. It is shown that the minimum initial on-site amplitude for which there is a collective escape increases with the nonlinear coupling. When the chain is forced at one end by a periodical excitation, the system exhibits supratransmission phenomenon in both lower and upper forbidden bandgaps, and, subsequently, it appears that the driving amplitude threshold for supratransmission in the upper forbidden bandgap frequency decreases with the nonlinear coupling.

Forward and backward propagating breathers in a DNA model with dipole-dipole long-range interactions.

The present study explores the existence and orbital stability of discrete bright breathers through the Joyeux-Buyukdagli DNA model incorporating long-range interactions (LRIs). The nonlinear Schrödinger equation is derived from a semidiscrete approximation and subsequently used to construct the targeted initial condition for numerical computations of the discrete breather. It appears that the interplay between the carrier wave frequency and the LRI induces stationary forward or backward propagating waves.

Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity.

The dynamics of DNA in the presence of uniform damping and periodic force is studied. The damped and driven Joyeux-Buyukdagli model is used to investigate the formation of intrinsic localized modes (ILMs). Branches of ILMs are identified as well as their orbital stabilities.

Discrete breathers dynamic in a model for DNA chain with a finite stacking enthalpy.

The nonlinear dynamics of a homogeneous DNA chain based on site-dependent finite stacking and pairing enthalpies is studied. A new variant of extended discrete nonlinear Schrödinger equation describing the dynamics of modulated wave is derived. The regions of discrete modulational instability of plane carrier waves are studied, and it appears that these zones depend strongly on the phonon frequency of Fourier's mode.