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A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…
In recent years, a new method for experimental nonlinear modal analysis has been developed, which is based on the extended periodic motion concept. The method is well suited to experimentally obtain amplitude-dependent modal properties…
The goal of the present paper is to study the viscoelastic wave equation with the time delay \[ |u_t|^\rho u_{tt}-\Delta u-\Delta u_{tt}+\int_0^tg(t-s)\Delta u(s)ds+\mu_1u_t(x,t)+\mu_2 u_t(x,t-\tau)=b|u|^{p-2}u\] under initial boundary…
We present a methodology for designing a dynamic controller with delayed output feedback for achieving non-collocated vibration suppression with a focus on the multi-frequency case. To synthesize the delay-based controller, we first remodel…
Previously, we demonstrated that the dynamics of kicked spin chains possess a remarkable duality property. The trace of the unitary evolution operator for $N$ spins at time $T$ is related to one of a non-unitary evolution operator for $T$…
The behaviour of a driven double well Duffing-van der Pol (DVP) oscillator for a specific parametric choice ($\mid \alpha \mid =\beta$) is studied. The existence of different attractors in the system parameters ($f-\omega$) domain is…
We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscillations to high-dimensional chaos. The oscillator uses electrooptic modulation…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
We study the long time behavior of isentropic compressible Euler equations with linear damping driven by a white-in-time noise, on a one-dimensional torus. We prove the existence of a statistically stationary solution in the class of weak…
The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The…
Oscillatory systems with time-delayed pulsatile feedback appear in various applied and theoretical research areas, and received a growing interest in the last years. For such systems, we report a remarkable scenario of destabilization of a…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
This paper investigates the decentralized stabilization problem for a class of interconnected systems in the presence of non-triangular structural uncertainties and time-varying parameters, where each subsystem exchanges information only…
The stabilization of nonautonomous parabolic equations is achieved by feedback inputs tuning a finite number of actuators, where it is assumed that the input is subject to a time delay. To overcome destabilizing effects of the time delay,…
Repetitive operations are widely conducted by automatic machines in industry. Periodic disturbances induced by the repetitive operations must be compensated to achieve precise functioning. In this paper, a periodic-disturbance observer…
The work fluctuations of an oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally and theoretically within the context of Fluctuation Theorems (FTs). The oscillator dynamics is…
The adiabatic approximation in time-dependent density functional theory (TDDFT) yields reliable excitation spectra with great efficiency in many cases, but fundamentally fails for states of double excitation character. We discuss how…
We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We…
In this paper, we consider the asymptotic behavior of weak solutions for nonclassical non-autonomous diffusion equations with a delay operator in time-dependent spaces when the nonlinear function $g$ satisfies subcritical exponent growth…
Energy efficiency is a crucial issue towards longterm deployment of compliant robots in the real world. In the context of variable impedance actuators (VIAs), one of the main focuses has been on improving energy efficiency through reduction…