Related papers: Multistability and localization in forced cyclic s…
Structural stiffness plays an important role in engineering design. The analysis of stiffness requires precise experiments and computational models that can be difficult or time-consuming to procure. A novel relation between modal and…
Domain specific localization of eigenstates has been a persistent observation for systems with local symmetries. The underlying mechanism for this localization behaviour has however remained elusive. We provide here an analysis of locally…
Two-dimensional spatially localized structures in the complex Ginzburg-Landau equation with 1:1 resonance are studied near the simultaneous occurrence of a steady front between two spatially homogeneous equilibria and a supercritical Turing…
Motivated by recent security issues in cyber-physical systems, this technical note studies the stabilization problem of networked control systems under Denial-of-Service (DoS) attacks. In particular, we consider to stabilize a nonlinear…
A piecewise-linear model with a single degree of freedom is derived from first principles for a driven vertical cantilever beam with a localized mass and symmetric stops. The resulting piecewise-linear dynamical system is smoothed by a…
The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in 1-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear…
Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled oscillators. We focus on Ginzburg--Landau equations with…
From cell development to space rockets, the mechanical stability of thin shells is crucial across many industrial and natural processes. However, predicting shells' failure properties remains an open challenge, owing to their sensitivity to…
A symmetric dissipative two-state system is asymptotically completely delocalized independent of the initial state. We show that driving-induced localization at long times can take place when both the bias and tunneling coupling energy are…
We study localized solutions for the nonlinear graph wave equation on finite arbitrary networks. Assuming a large amplitude localized initial condition on one node of the graph, we approximate its evolution by the Duffing equation. The rest…
A periodic perturbation generates a complicated dynamics close to separatrices and saddle points. We construct an asymptotic solution which is close to the separatrix for the unperturbed Duffing's oscillator over a long time. This solution…
We investigate energy transfer and localization in a linear time-invariant oscillator chain weakly coupled to a forced nonlinear actuator. Two types of perturbation are studied: (1) harmonic forcing with a constant frequency is applied to…
A weak-localization effect has been studied in macroscopically inhomogeneous 2D system. It is shown, that although the real phase breaking length tends to infinity when the temperature tends to zero, such a system can reveal a saturated…
We theoretically investigate the dynamics, bifurcation structure and stability of quadratic dark localized dissipative states arising in cavity enhanced second-harmonic generation. These states, formed through the locking of plane front…
Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localised) instability when one or both of its lateral surfaces are under sufficient surface tension.…
Solitons are typically stable objects in 1D models, but their straightforward extensions to 2D and 3D settings tend to be unstable. In particular, the ubiquitous nonlinear Schroedinger (NLS) equation with the cubic self-focusing, creates…
We apply the well-established theoretical method developed for geometrical nonlinearities of micro/nano-mechanical clamped beams to circular drums. The calculation is performed under the same hypotheses, the extra difficulty being to…
Fully localised patterns involving cellular hexagons or squares have been found experimentally and numerically in various continuum models. However, there is currently no mathematical theory for the emergence of these localised cellular…
Decay to asymptotic steady state in one-dimensional logistic-like mappings is characterized by considering a phenomenological description supported by numerical simulations and confirmed by a theoretical description. As the control…
We demonstrate that nonlinearity plays a constructive role in supporting the robustness of dynamical localization in a model which is discrete, in one dimension and continuous in the orthogonal one. In the linear regime, time-periodic…