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Waveguides subject to spatiotemporal modulations are known to exhibit nonreciprocal vibration transmission, whereby interchanging the locations of the source and receiver change the end-to-end transmission characteristics. The scenario of…

Neural circuits exhibit remarkable computational flexibility, enabling adaptive responses to noisy and ever-changing environmental cues. A fundamental question in neuroscience concerns how a wide range of behaviors can emerge from a…

The nonlinear stage of modulational instability in optical fibers induced by a wide and easily accessible class of localized perturbations is studied using the nonlinear Schrodinger equation. It is showed that the development of associated…

This paper investigates the complex nonlinear dynamics of an optomechanical system featuring an optical cavity coupled to two mechanical resonators interconnected by a phase-dependent interaction. We specifically explore the role of this…

We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…

We investigate the modulational instability of plane waves in quadratic nonlinear materials with linear and nonlinear quasi-phase-matching gratings. Exact Floquet calculations, confirmed by numerical simulations, show that the periodicity…

In contrast to conservative systems, in nonlinear media with gain and loss the dynamics of localized topological structures can exhibit unique features that can be controlled externally. We propose a robust mechanism to perform topological…

To explore resonance phenomena in the nonlinear region, we show by experimental measurements and theoretical analyses that resonance happens in modulation instability (MI) from non-instantaneous nonlinearities in photorefractive crystals.…

A sudden change in dynamics produces large errors leading to increases in muscle co-contraction and feedback gains during early adaptation. We previously proposed that internal model uncertainty drives these changes, whereby the…

This book chapter describes the dynamics of a modulated oscillator for resonant and nonresonant modulation. Two types of resonant modulation are considered: additive, with frequency close to the oscillator eigenfrequency, and parametric,…

We present an optical fiber experiment in which we examine the space-time evolution of a modulationally unstable plane wave initially perturbed by a small noise. Using a recirculating fiber loop as experimental platform, we report the…

Modal methods are a long-standing approach to physical modelling synthesis. Extensions to nonlinear problems are possible, leading to coupled nonlinear systems of ordinary differential equations. Recent work in scalar auxiliary variable…

In this paper, modulation instability and nonlinear supratransmission are investigated in a one-dimensional chain of atoms using cubic-quartic nonlinearity coefficients. As a result, we establish the discrete nonlinear evolution equation by…

Modulation instability (MI) in continuous media described by a system of two cubic-quintic nonlinear Schr\"odinger equations (NLSE) has been investigated with a focus on revealing the contribution of the quintic nonlinearity to the…

We theoretically propose a nonlinear spin-wave Doppler effect, in which the time-dependent motion of a magnetic energy boundary acts as an active frequency modulator, directly converting boundary-induced phase dynamics into instantaneous…

We report nonlinear behavior in the motion of driven nanowire cantilevers. The nonlinearity can be described by the Duffing equation and is used to demonstrate mechanical mixing of two distinct excitation frequencies. Furthermore, we…

Modulation instability is a phenomenon of spontaneous pattern formation in nonlinear media, oftentimes leading to an unpredictable behaviour and a degradation of a signal of interest. We propose an approach based on reinforcement learning…

We address the interactions between optical solitons in the system with longitudinally varying nonlocality degree and nonlinearity strength. We consider a physical model describing light propagation in nematic liquid crystals featuring a…

Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…

Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…