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Diffusion models have recently exhibited remarkable abilities to synthesize striking image samples since the introduction of denoising diffusion probabilistic models (DDPMs). Their key idea is to disrupt images into noise through a fixed…

For sufficiently wide ranges of applied control signals (control voltages), MEMS and piezoelectric Deformable Mirrors (DMs), exhibit nonlinear behavior. The nonlinear behavior manifests itself in nonlinear actuator couplings, nonlinear…

A theory of nonlinear signal propagation in multi-span wavelength division multiplexed coherent transmission systems that employ the semiconductor optical amplifier as in-line amplifiers is presented for the first time. The rigorous…

The qualitative study of dynamical systems using bifurcation theory is key to understanding systems from biological clocks and neurons to physical phase transitions. Data generated from such systems can feature complex transients, an…

Discontinuous piecewise differential systems exhibit dynamical behaviors with no counterpart in smooth systems, particularly in the presence of nonsmooth switching structures. In this work, we extend previous results for systems separated…

Discrete time crystals are a special phase of matter in which time translational symmetry is broken through a periodic driving pulse. Here, we first propose and characterize an effective mechanism to generate a stable discrete time crystal…

In this paper, we present the linear decomposition method (LDM), which we developed to detect and analyze pulsar profile variations and mode changing behaviour. We developed LDM utilizing the likelihood function approach assuming the…

Quantum processes of inherent dynamical nature, such as quantum walks (QWs), defy a description in terms of an equilibrium statistical physics ensemble. Up to now, it has remained a key challenge to identify general principles behind the…

The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…

Optomechanical systems attract a lot of attention because they provide a novel platform for quantum measurements, transduction, hybrid systems, and fundamental studies of quantum physics. Their classical nonlinear dynamics is surprisingly…

Significant amplitude-independent and passive non-reciprocal wave motion can be achieved in a one dimensional (1D) discrete chain of masses and springs with bilinear elastic stiffness. Some fundamental asymmetric spatial modulations of the…

The new phenomenon of semiquantum chaos is analyzed in a classically regular double-well oscillator model. Here it arises from a doubling of the number of effectively classical degrees of freedom, which are nonlinearly coupled in a Gaussian…

Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…

A novel control design approach for general nonlinear systems is described in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. Extensive…

Current simulations of ultraviolet-visible absorption lineshapes, and dynamics of condensed phase systems, largely adopt a harmonic description to model vibrations. Often, this involves a model of displaced harmonic oscillators that have…

We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a new time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the frame of statistical ensemble of quantum…

A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…

This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period…

This article is a short review of the recent results on properties of nonlinear fractional maps which are maps with power- or asymptotically power-law memory. These maps demonstrate the new type of attractors - cascade of bifurcations type…

The non-commutative nature of quantum mechanics imposes fundamental constraints on system dynamics, which, in the linear realm, are manifested through the physical realizability conditions on system matrices. These restrictions give system…