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Domains walls and topological defects in ferroelectric materials have emerged as a powerful new paradigm for functional electronic devices including memory and logic. Similarly, wall interactions and dynamics underpin a broad range of…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
Magnetic domain walls in antiferromagnets have been proposed as key components for faster conventional information processing, thanks to their enhanced stability and ultrafast propagation. However, how non-conventional computing methods…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
We present a new method of analysis of measure-preserving dynamical systems, based on frequency analysis and ergodic theory, which extends our earlier work [1]. Our method employs the novel concept of harmonic time average [2], and is…
We have introduced a mechanism for synchronizing chaotic systems by one way coupling with a variable delay that is reset at finite intervals. Here we extend this method to time delay systems and suggest a new cryptosystem based on this. We…
This paper introduces a novel stabilization control strategy for linear time-invariant systems affected by known time-varying measurement delays and matched unknown nonlinear disturbances, which may encompass actuator faults. It is…
We propose a numerical method to solve general hyperbolic systems in any space dimension using forward Euler time stepping and continuous finite elements on non-uniform grids. The properties of the method are based on the introduction of an…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
We provide a solution to the heretofore open problem of stabilization of systems with arbitrarily long delays at the input and output of a nonlinear system using output feedback only. The solution is global, employs the predictor approach…
This paper focuses on time-varying delayed stochastic differential systems with stochastically switching parameters formulated by a unified switching behavior combining a discrete adapted process and a Cox process. Unlike prior studies…
Using a variational method, we prove the existence of heteroclinic solutions for a 6dimensional system of ordinary differential equations. We derive this system from the classical B{\'e}nard-Rayleigh problem near the convective instability…
We demonstrate that the evolution of wall-like inhomogeneities in run-away potentials, characteristic of dynamical supersymmetry breaking and moduli stabilisation, is very similar to the evolution of domain wall networks associated with…
We present an event-triggered control strategy for stabilizing a scalar, continuous-time, time-invariant, linear system over a digital communication channel having bounded delay, and in the presence of bounded system disturbance. We propose…
Domain wall propagation has been measured in continuous, weakly disordered, quasi-two-dimensional, Ising-like magnetic layers that are subject to spatially periodic domain wall pinning potentials. The potentials are generated…
We investigate the role of a quasiperiodically driven electric field in a one-dimensional disordered fermionic chain. In the clean non-interacting case, we show the emergence of dynamical localization - a phenomenon previously known to…
The dynamics of a multiferroic domain wall in which an electric field can couple to the magnetization via inhomogeneous magnetoelectric interaction is investigated by the collective-coordinate framework. We show how the electric field is…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…