Periodic driving shape controls energy transmission.

In the early 2000s, Geniet and Leon [Phys. Rev. Lett. 89, 134102 (2002)0031-900710.1103/PhysRevLett.89.134102] discovered the nonlinear supratransmission (NST) in a medium with a forbidden frequency band gap. It is a process in which nonlinear structures are created by a sinusoidal harmonic boundary condition imposed at a frequency in the band gap. The present study extends this concept and shows that an optimal shape of a periodic nonsinusoidal excitation may induce (or inhibit) energy flow through the lattice below (or above) the NST threshold, demonstrating that nonlinear supratransmission is reliant not only on the driving amplitude but also on its shape. This is evidenced through numerical simulations and mathematical calculations varying the excitation signal shape in the Fermi-Pasta-Ulam case study. Setting the shape parameter to zero recovers the results of the literature in relation to the sinusoidal signal.

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. In the lower forbidden band, the dependence of the supratransmission threshold on the mass ratio (µ=m/M) has been evidenced and it appears that for large (small) values of µ, that is µ>60%, the coupling between the two modes must (must not) be considered. Numerical explorations were subsequently performed with an emphasis on the dependence of the threshold on the driving frequency and also on the mass of the driven particle (light or heavy). A good agreement is found between the numerical and analytical thresholds. For the limit case where all the masses are identical, the results of the monoatomic FPU previously found in the literature are recovered.

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. A maximum amplification also occurs at a moderate level of MFD, indicating that the response exhibits a nonmonotonic sensitivity to MFD. The MFD-enhanced response depends mainly on the signal intensity but not on the signal frequency or the network topology. The analytical investigation provides a simplified model to study the mechanism underlying this resonancelike behavior. It is shown that by modifying the bistability nature of the potential energy, the mean field density can promote well-to-well oscillations and larger amplitude motions. Finally, the robustness of this phenomenon to various signal waveforms is examined. It can therefore be used alternatively to efficiently amplify weak signals in practical situations with large network sizes.

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. In contrast to homogeneous coupling, network size plays a crucial role in reducing this critical value. This behavior can be traced back to the steady-state destabilization through a Hopf's bifurcation, which occurs for impurity strengths below this threshold. This effect is illustrated across different mean-field coupled networks and is supported by simulations and theoretical analysis. Since local inhomogeneities are ubiquitous and often unavoidable, such imperfections can be an unexpected source of oscillation control.

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. For critical values of the LRI, stationary waves can occur out of the center/edge of the first Brillouin zone. The predicted breathers differ in their robustness and mobility for specific carrier-wave frequency and LRI. In all cases, semianalytical predictions agree with numerical simulations.

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. A study of the effect of inhomogeneity introduced into the DNA lattice and its ability to control chaotic behavior is conducted. It is seen that a single defect in the chain can induce synchronized spatiotemporal patterns, despite the fact that the entire set of oscillators and the impurity are chaotic when uncoupled. It is also shown that the periodic excitation applied on a specific site can drive the whole lattice into chaotic or regular spatial and temporal patterns.

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. The staggered/unstaggered discrete breather (SDB/USDB) is obtained straightforwardly without the staggering transformation, and it is demonstrated that SDBs are less unstable than USDB. The instability of discrete multi-humped SDB/USDB solution does not depend on the number of peaks of the discrete breather (DB). By using the concept of Peierls-Nabarro energy barrier, it appears that the low-frequency DBs are more mobile.