On some applications of vibrational resonance on noisy image perception: the role of the perturbation parameters

In this paper, we first propose a brief overview of nonlinear resonance applications in the context of image processing. Next, we introduce a threshold detector based on these resonance properties to investigate the perception of subthreshold noisy images. By considering a random perturbation, we revisit the well-known stochastic resonance (SR) detector whose best performances are achieved when the noise intensity is tuned to an optimal value. We then introduce a vibrational resonance detector by replacing the noisy perturbation with a spatial high-frequency signal. To enhance the image perception through this detector, it is shown that the noise level of the input images must be lower than the optimal noise value of the SR-based detector. Under these conditions, considering the same noise level for both detectors, we establish that the vibrational resonance (VR)-based detector significantly outperforms the SR-based detector in terms of image perception. Moreover, we show that whatever the perturbation amplitude, the best perception through the VR detector is ensured when the perturbation frequency exceeds the image size. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.

Experimental observation of the generation of cutoff solitons in a discrete LC nonlinear electrical line

We address the problem of supratransmission of waves in a discrete nonlinear system, driven at one end by a periodic excitation at a frequency lying above the phonon band edge. In an experimental electrical transmission line made of 200 inductance-capacitance LC cells, we establish the existence of a voltage threshold for a supratransmission enabling the generation and propagation of cut-off solitons within the line. The decisive role of modulational instability in the onset and development of the process of generation of cut-off solitons is clearly highlighted. The phenomenon of dissipation is identified as being particularly harmful for the soliton generation, but we show that its impact can be managed by a proper choice of the amplitude of the voltage excitation of the system.

Cutoff solitons and bistability of the discrete inductance-capacitance electrical line: theory and experiments

A discrete nonlinear system driven at one end by a periodic excitation of frequency above the upper band edge (the discreteness induced cutoff) is shown to be a means to (1) generate propagating breather excitations in a long chain and (2) reveal the bistable property of a short chain. After detailed numerical verifications, the bistability prediction is demonstrated experimentally on an electrical transmission line made of 18 inductance-capacitance (LC) cells. The numerical simulations of the LC -line model allow us also to verify the breather generation prediction with a striking accuracy.

Wave front propagation failure in an inhomogeneous discrete Nagumo chain: theory and experiments

The phenomenon of wave propagation failure in a discrete inhomogeneous Nagumo equation is investigated. It is found that the propagation failure occurs not only for small coupling coefficients but as well for an abrupt change of the interelement coupling. The investigation includes the study of the phase space of the system, numerical simulations, and real experiments with a nonlinear electrical lattice.

Theoretical and experimental study of two discrete coupled Nagumo chains

We analyze front wave (kink and antikink) propagation and pattern formation in a system composed of two coupled discrete Nagumo chains using analytical and numerical methods. In the case of homogeneous interaction among the chains, we show the possibility of the effective control on wave propagation. In addition, physical experiments on electrical chains confirm all theoretical behaviors.

Propagation failure in discrete bistable reaction-diffusion systems: theory and experiments

Wave front propagation failure is investigated in discrete bistable reaction-diffusion systems. We present a theoretical approach including dissipative effects and leading to an analytical expression of the critical coupling beyond which front propagation can occur as a function of the nonlinearity threshold parameter. Our theoretical predictions are confirmed by numerical simulations and experimental results on an equivalent electrical diffusive lattice.

Dissipative lattice model with exact traveling discrete kink-soliton solutions: discrete breather generation and reaction diffusion regime

We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the non-dissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a discrete reaction diffusion equation; our simulations show that, for a given potential shape, discrete wave fronts can travel without experiencing any propagation failure but their collisions are inelastic.