Congratulations to Usama Bello Ibrahim who successfully defended his thesis on Monday and thus obtained the rank of doctor.

Thesis title :

Nonlinear resonances and some of their applications to information processing

Abstract :

The study of resonance phenomena in nonlinear dynamical systems has drawn considerable attention for years. The most studied nonlinear resonance is undoubtedly the famous stochastic resonance, which consists of perturbing a nonlinear system with an appropriate amount of noise to enhance the detection of a subthreshold input signal. Since the introduction of stochastic resonance in the context of climate dynamics, it was later observed that a deterministic high frequency perturbation can replace noise leading to vibrational resonance. Even if this latter resonance was investigated in many areas of science for more than two decades now, it is still receiving attentions. It is the subject of this thesis, which numerically analyzes
the occurrence of this phenomenon in two different nonlinear systems, and which suggests applications in the context of subthreshold images perception. First, we analyze the motion of a particle with a given mass which is submitted to a nonlinear force deriving from a double-well potential. For both considered cases of linear and nonlinear space-dependent damping, we establish that there exists a critical mass beyond which vibrational resonance ceases to exist. Next, we analyze how the nonlinearity affects vibrational resonance in the Chua’s circuit model. Especially, we show that better resonances can be achieved when Chua’s system experiences a truncated sinusoidal nonlinearity instead of the conventional sawtooth nonlinearity. Moreover, when the system driving consists of two close low frequencies, we observe that the high frequency perturbation can induce resonances at the two input low frequencies but also at a lower frequency via the mechanisms of vibrational resonance and ghost-vibrational resonance. Lastly, we consider the perception of subthreshold images through perturbed threshold detectors. In terms of image perception, we show that detectors which are based on vibrational resonance clearly outperform detectors based on stochastic resonance