Related papers: From dynamical systems with time-varying delay to …

We present the control of the high-dimensional chaos, with possibly a large number of positive Lyapunov-exponents, of unknown time-delay systems to an arbitrary goal dynamics. We give an existence-and-uniqueness theorem for the control…

The Miles-Krasnopolskaya system is considered, which is used to study the nonlinear interaction of a tank with a liquid and the source of excitation of its oscillations. Additionally, delay time of impulse from the source of excitation of…

This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…

In this paper, we study the well-posedness and approximate controllability of a class of network systems having delays and controls at the boundary conditions. The particularity of this work is that the network system is defined on infinite…

In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…

We extend the Pyragas time-delayed feedback control (TDFC) to apply it to random dynamical systems and introduce an extended classification based on Lyapunov exponents and trajectory fluctuations. We demonstrate the applicability of this…

Solving an output consensus problem in multi-agent systems is often hindered by multiple time-variant delays. To address such fundamental problems over time, we present a new optimal time-variant distributed control for linearly perturbed…

We consider consensus of multi-agent systems as a dual problem to Markov processes. Based on an exchange of relevant notions and results between the two fields, we present a uniform framework which admits the introduction and treatment of…

Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…

As a hybrid of techniques from open-loop and feedback control, Lyapunov control has the advantage that it is free from the measurement-induced decoherence but it includes the system's instantaneous message in the control loop. Often, the…

Dynamic Mode Decomposition (DMD) has become synonymous with the Koopman operator, where continuous time dynamics are examined through a discrete time proxy determined by a fixed timestep using Koopman (i.e. composition) operators. Using the…

We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…

Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…

The Koopman Operator (KO) is a mathematical construct that maps nonlinear (state space) dynamics to corresponding linear dynamics in an infinite-dimensional functional space. For practical applications, finite-dimensional approximations can…

We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…

Time-delay embedding is a technique that uses snapshots of state history over time to build a linear state space model of a nonlinear smooth system. We demonstrate that periodic non-smooth or hybrid system can also be modeled as a linear…

We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…

In this work, we propose a rigorous method for implementing predictor feedback controllers in nonlinear systems with unknown and arbitrarily long actuator delays. To address the analytically intractable nature of the predictor, we…

In this paper, we study the dynamics and stability of a fundamental power system model when a time delay is imposed on the excitation of the generator. It is observed that sustained oscillations can arise in an otherwise stable power system…

In this contribution, the estimates for the response of time delay systems with nonlinear homogeneous right-hand side of degree strictly greater than one are constructed. The existing results obtained via the Lyapunov--Razumikhin approach…