Related papers: Boundary-driven delayed-feedback control of spatio…
This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design…
This paper is concerned with boundary stabilization of two-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with…
We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a…
This study proposes an effective theoretical framework for non-adiabatic parametric excitation in structured media, incorporating a nonlinear frequency regulator U as a stabilizing mechanism. We introduce the non-adiabaticity parameter as a…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient coupled reaction-diffusion systems was solved by means of the backstepping method. The extension of this result to systems with advection terms and…
We analyze the control of frequency for a synchronized inhibitory neuronal network. The analysis is done for a reduced membrane model with a biophysically-based synaptic influence. We argue that such a reduced model can quantitatively…
We study gravitationally unstable, transient, diffusive boundary layers in porous media using modal and nonmodal stability methods. Using nonmodal stability theory, we demonstrate that both the onset of linear instabilities and the shape of…
We study the control of noise-induced spatio-temporal current density patterns in a semiconductor nanostructure (double barrier resonant tunnelling diode) by multiple time-delayed feedback. We find much more pronounced resonant features of…
We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control…
In a weakly excitable medium, characterized by a large threshold stimulus, the free end of an isolated broken plane wave (wave tip) can either rotate (steadily or unsteadily) around a large excitable core, thereby producing a spiral…
Understanding the relationship between symmetry breaking, system properties, and instabilities has been a problem of longstanding scientific interest. Symmetry-breaking instabilities underlie the formation of important patterns in driven…
Periodically forced, oscillatory fluid flows have been the focus of intense research for decades due to their richness as a nonlinear dynamical system and their relevance to applications in transportation, aeronautics, and energy…
This technical note is concerned with boundary stabilization of multi-dimensional discrete-velocity kinetic models. By exploiting a certain stability structure of the models and adapting an appropriate Lyapunov functional, we derive…
The discovery of topological insulators has opened new prospects for robust signal transport for electronic, phononic, and photonic devices. Though transport of topological protected edge states is robust to disorder, large fluctuations and…
Dynamic phenomena in social and biological sciences can often be modeled by employing reaction-diffusion equations. When addressing the control of these modes, from a mathematical viewpoint one of the main challenges is that, because of the…
Controlling spatiotemporal chaos in excitable media by applying low-amplitude perturbations {\em locally} is of immediate applicability, e.g., in treating ventricular fibrillation, a fatal disturbance in the normal rhythmic functioning of…
Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This…
We investigate the impact of the domain shape on wave propagation in excitable media. Channelled domains with sinusoidal boundaries are considered. Trains of fronts generated periodically at an extreme of the channel are found to adopt a…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…