Impulse-induced generation of stationary and moving discrete breathers in nonlinear oscillator networks

Abstract

We study discrete breathers in prototypical nonlinear oscillator networks subjected to nonharmonic zero-mean periodic excitations. We show how the generation of stationary and moving discrete breathers are optimally controlled by solely varying the impulse transmitted by the periodic excitations, while keeping constant the excitation's amplitude and period. Our theoretical and numerical results show that the enhancer effect of increasing values of the excitation's impulse, in the sense of facilitating the generation of stationary and moving breathers, is due to a correlative increase of the breather's action and energy.

Induced localized nonlinear modes in an electrical lattice

“…where t * , t * * ∈ [0, T /2]. According to [15], the role of the external periodic excitation F (t) is played by the explicit timedependent function dV s (t)/dt , and hence I =…”

“…where N (m) is a normalization factor [15], K(m) is the complete elliptic integral of the first kind, and sn (·; m) , dn (·; m) are Jacobian elliptic functions of parameter m. Thus, one can change the PEs' waveform by solely varying their shape parameter m between 0 and 1 while keeping constant their amplitude and period. If parameter m is small enough (m ∈ [0, 0.8]), a good approximation of these functions is given by the first two terms of its Fourier series which reads…”

“…where cn(·; m) is the Jacobian elliptic function of parameter m, and hence they are shift-symmetric functions: V (m = 0) as functions of the shape parameter m. Solid (black) and dashed (blue) lines correspond to the functions (14) and (15) while dotted (black) and dash-dot (blue) lines correspond to the first Fourier coefficient of (4) and (5), respectively.…”

Bouncing states of a droplet on a liquid surface under generalized forcing

“…i.e., I is given by the (absolute) difference between the slopes of the FS at two of its consecutive zeros. The relevance of the signal's impulse has been observed previously in quite different physical contexts, such as adiabatically ac driven periodic Hamiltonian systems [13], chaotic dynamics of a pumpmodulation Nd:YVO 4 laser [14], ratchet transport [15][16][17][18], discrete breathers in nonlinear oscillator networks [19], topological amplification effects in scale-free networks of signaling devices [20], driven two-level systems and periodically curved waveguide arrays [21], and control of chaos in damped driven systems by secondary periodic excitations [22]. FIG.…”

Suppressing Chaos in Damped Driven Systems by Non-Harmonic Excitations: Experimental Robustness Against Potential's Mismatches

“…We compare the predictions from this theoretical model with experimental results from a second order analogue electrical circuit having an extremely simple two-well potential, which is similar but not identical to that of the two-well Duffing oscillator. The importance of the excitation's impulse has been previously confirmed in different physical contexts, such as space-periodic Hamiltonian systems [32], laser systems [33], directed transport by symmetry breaking [34][35][36][37], oscillator networks [38], scale-free networks of signaling devices [39], control of wave-packet localization [40], suppression of chaos in dissipative driven systems [25], and bouncing droplets [41].…”