Related papers: The non-anticipation of the asynchronous systems
This thesis is devoted to the study of physical systems embedded within the field of non-equilibrium statistical mechanics. Specifically, the state of the systems of interest constitutes a stochastic process that can be externally driven by…
The chaotic synchronization between two bi-directionally coupled external cavity single-mode semiconductor lasers is investigated. Numerical simulation shows that anticipating synchronization and lag synchronization coexist in certain…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
Given a discrete-state continuous-time reactive system, like a digital circuit, the classical approach is to first model it as a state transition system and then prove its properties. Our contribution advocates a different approach: to…
Feedback is an essential composition operator in many classes of reactive and other systems. This paper studies feedback in the context of compositional theories with refinement. Such theories allow to reason about systems on a…
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…
In this article, we consider a dynamic model of a three-phase power system including nonlinear generator dynamics, transmission line dynamics, and static nonlinear loads. We define a synchronous steady-state behavior which corresponds to…
The present paper explores the synchronization scenario of hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment. We show that depending upon the coupling parameters a hyperchaotic time-delayed system…
Synchronization, the emergence of spontaneous order in coupled systems, is of fundamental importance in both physical and biological systems. We demonstrate the synchronization of two dissimilar silicon nitride micromechanical oscillators,…
Non-stationary systems are found throughout the world, from climate patterns under the influence of variation in carbon dioxide concentration, to brain dynamics driven by ascending neuromodulation. Accordingly, there is a need for methods…
In control theory, a system which has output depending only on the present and past values of the input is said to be causal (or nonanticipative). Respectively, a system is acausal (or non-causal) if its output depends on future inputs as…
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more…
Non-ideal deterministic system "tank with liquid-electric motor" is studied. Two delay-approximation models are considered. Impact of the delay on the emergence, evolution and disappearance of regular and chaotic limit sets (attractors) of…
Standard dynamical systems theory is centred around the coordinate-invariant asymptotic-time properties of autonomous systems. We identify three limitations of this approach. Firstly, we discuss how the traditional approach cannot take into…
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
This manuscript contains technical details and proofs of recent results developed by the authors, pertaining to the design of nonlinear controllers from the experimental data measured on an existing feedback control system.
Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…
In these lectures, we shall present some remarkable results that have been obtained for systems far from equilibrium during the last two decades. We shall put a special emphasis on the concept of large deviation functions that provide us…
With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…