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The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when…
Thermoacoustic instabilities in gas turbines and aeroengine combustors falls within the category of complex systems. They can be described phenomenologically using nonlinear stochastic differential equations, which constitute the grounds…
This paper considers the robustness of an uncertain nonlinear system along a finite-horizon trajectory. The uncertain system is modeled as a connection of a nonlinear system and a perturbation. The analysis relies on three ingredients.…
Warning signs for tipping points (or critical transitions) have been very actively studied. Although the theory has been applied successfully in models and in experiments for many complex systems such as for tipping in climate systems,…
The physics of critical phenomena in a many-body system far from thermal equilibrium is an interesting and important issue to be addressed both experimentally and theoretically. The trapped cold atoms have been actively used as a clean and…
In recent years there have been significant advances in the study of many-body interactions between atoms and light confined to optical cavities. One model which has received widespread attention of late is the Dicke model, which under…
We provide a rigorous justification of various kinetic regimes exhibited by the nonlinear Schr\"{o}dinger equation with an additive stochastic forcing and a viscous dissipation. The importance of such damped-driven models stems from their…
In this letter, we experimentally demonstrate an efficient scheme to regulate the behaviour of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term…
Most prior works studying tidal interactions in tight star/planet or star/star binary systems have employed linear theory of a viscous fluid in a uniformly-rotating two-dimensional spherical shell. However, compact systems may have…
The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational…
An accurate experimental and theoretical study has been performed about a phenomenon, not previously reported in the literature, occurring in highly viscous liquids: the formation of a definite pipe structure induced by the passage of a…
We investigate the time-periodic solutions to the nonlinear wave and beam equations and uncover their intricate, fractal-like structure. In particular, we identify a new class of large-energy solutions with complex mode compositions and…
We develop an early-warning signal for bifurcations of one-dimensional random difference equations with additive bounded noise, based on the asymptotic behaviour of the stationary density near a boundary of its support. We demonstrate the…
The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…
We present a novel class of nonlinear dynamical systems - a hybrid of relativistic quantum and classical systems, and demonstrate that multistability is ubiquitous. A representative setting is coupled systems of a topological insulator and…
Modeling fluid turbulence using a 'skeleton' of coherent structures has traditionally progressed by focusing on a few canonical experiments, such as pipe flow and Taylor-Couette flow. We here consider an alternative canonical experiment,…
ONE of the main goals in the development of theory of chaotic dynamical system has been to make progress in understanding of turbulence. The attempts to related turbulence to chaotic motion got strong impetus from the celebrated paper by…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
Nonlinear dynamical systems may be exposed to tipping points, critical thresholds at which small changes in the external inputs or in the systems parameters abruptly shift the system to an alternative state with a contrasting dynamical…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…