Related papers: Forced Frequency Locking for Semilinear Dissipativ…
We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency.…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
Quantum dots in GaAs/InGaAs structures have been proposed as a candidate system for realizing quantum computing. The short coherence time of the electronic quantum state that arises from coupling to the nuclei of the substrate is…
In this article a stabilizing feedback control is computed for a semilinear parabolic partial differential equation utilizing a nonlinear model predictive (NMPC) method. In each level of the NMPC algorithm the finite time horizon open loop…
We study a two-dimensional fermionic QFT used to model 1D strongly correlated electrons in the presence of a time-dependent impurity that drives the system out of equilibrium. In contrast to previous investigations, we consider a dynamic…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
While polymer solutions lack the mechanical stability only transiently cross-linked networks can fulfill the competing requirements of structural stability and maximal energy dissipation. Here, we show that transient cross-links entail…
We propose an alternative to the standard mechanisms for the formation of rogue waves in a non-conservative, nonlinear lattice dynamical system. We consider an ODE system that features regular periodic bursting arising from forced symmetry…
We propose a time-delayed model for the study of active mode-locking that is valid for large values of the round-trip gain and losses. It allows us to access the typical regimes encountered in semiconductor lasers and to perform an extended…
We present here a brief overview of our work in developing a convolutionless quantum master equation approach suitable for mesoscopic sized systems. Our final equation can be used in the regimes where the golden rule approach is not…
The theory of stationary spatially localized patterns in dissipative systems driven by time-independent forcing is well developed. With time-periodic forcing related but time-dependent structures may result. These may consist of breathing…
We excite spin-waves with spatially inhomogeneous pulses and study the resulting frequency shifts of a chip-scale atomic clock of trapped $^{87}$Rb. The density-dependent frequency shifts of the hyperfine transition simulate the s-wave…
Forced oscillation (FO) is a significant concern threating the power system stability. Its mechanisms are mostly studied via linear models. However, FO amplitude is increasing, e.g., Nordic and Western American FOs, which can stimulate…
In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…
We are concerned with the dynamical behavior of solutions to semilinear wave systems with time-varying damping and nonconvex force potential. Our result shows that the dynamical behavior of solution is asymptotically stable without any…
The periodic solutions of a type of nonlinear hyperbolic partial differential equations with a localized nonlinearity are investigated. For instance, these equations are known to describe several acoustical systems with fluid-structure…
We consider an array of nearest-neighbor coupled nonlinear autonomous oscillators with quenched random frequencies and purely conservative coupling. We show that global phase-locked states emerge in finite lattices and study numerically…
We report a spectrum of exotic frequency-locked states in a ring of phase oscillators with pure three-body interactions. For identical oscillators, the system hosts a vast multiplicity of stable quantized frequency-locked states without…
In this paper, we employed linear algebra and functional analysis to determine necessary and sufficient conditions for oscillation-free and stable solutions to linear and nonlinear parabolic partial differential equations. We applied…
Nonlinear oscillators are commonly encountered in a wide range of physical and engineering systems, exhibiting rich and complex dynamics. Among these, the Van der Pol oscillator is well known for its self-sustained limit cycle behavior.…