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We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Artificial time delay controller was conceptualised for nonlinear systems to reduce dependency on precise system modelling unlike the conventional adaptive and robust control strategies. In this approach unknown dynamics is compensated by…
The asynchronous systems $f$ are the models of the asynchronous circuits from digital electrical engineering. They are multi-valued functions that associate to each input $u:\mathbf{R}\to \{0,1\}^{m}$ a set of states $x\in f(u),$ where…
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…
We consider two identical oscillators with weak, time delayed coupling. We start with a general system of delay differential equations then reduce it to a phase model. With the assumption of large time delay, the resulting phase model has…
As the process technologies scale into deep submicron region, crosstalk delay is becoming increasingly severe, especially for global on-chip buses. To cope with this problem, accurate delay models of coupled interconnects are needed. In…
The problem of synchronization in heterogeneous networks of linear systems with nonlinear delayed diffusive coupling is considered. The network is presented in new coordinates mean-field dynamics and synchronization errors. Thus the problem…
Collaboration between interconnected cyber-physical systems is becoming increasingly pervasive. Time-delays in communication channels between such systems are known to induce catastrophic failure modes, like high frequency oscillations in…
Delays associated with elementary interaction processes are investigated. The case of broad resonances is discussed in the context of reaction simulations.
Time-delay systems are an important class of dynamical systems which provide a solid mathematical framework to deal with many application domains of interest ranging from biology, chemical, electrical, and mechanical engineering, to…
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying…
In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
Existence of a new type of oscillating synchronization that oscillates between three different types of synchronizations (anticipatory, complete and lag synchronizations) is identified in unidirectionally coupled nonlinear time-delay…
Experimental observations of typical kinds of synchronization transitions are reported in unidirectionally coupled time-delay electronic circuits with a threshold nonlinearity and two time delays, namely feedback delay $\tau_1$ and coupling…
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…
A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…
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…
Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…