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Classical models of pattern formation are based on diffusion-driven instability (DDI) of constant stationary solutions of reaction-diffusion equations, which leads to emergence of stable, regular Turing patterns formed around that…
We present a singular perturbation theory applicable to systems with hybrid boundary layer systems and hybrid reduced systems {with} jumps from the boundary layer manifold. First, we prove practical attractivity of an adequate attractor set…
We study the spread of a quantum-mechanical wavepacket in a noisy environment, modeled using a tight-binding Hamiltonian. Despite the coherent dynamics, the fluctuating environment may give rise to diffusive behavior. When correlations…
The aim of this paper is to investigate the use of Pyragas control on the stability of stationary, localised coherent structures in a general class of two-component, singularly perturbed, reaction-diffusion systems. We use noninvasive…
Learning-based control of linear systems received a lot of attentions recently. In popular settings, the true dynamical models are unknown to the decision-maker and need to be interactively learned by applying control inputs to the systems.…
In this paper, we derive a stability result for $L_1$ and $L_{\infty}$ perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth,…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
This paper studies the stability and dynamic control of underlay mobile edge networks. First, the stability region for a multiuser edge network is obtained under the assumption of full channel state information. This result provides a…
We investigate intermittent diffusion using cycle expansions, and show that a truncation based on cycle stability achieves reasonable convergence.
Stability and control of a non-linear system represent an important system configuration that frequently arises in practical engineering. Stability covers a vast range of systems that do not obey the superposition principle and applies to…
We develop a diffusion approximation for systems subject to fast random resetting by small amplitudes. Equivalently, this describes systems with frequent but small catastrophes. We demonstrate the validity of the approximation by computing…
Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to…
In this paper, we utilize event-triggered coupling configuration to realize synchronization of linearly coupled dynamical systems. Here, the diffusion couplings are set up from the latest observations of the nodes of its neighborhood and…
In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…
The linearization principle states that the stability (or instability) of solutions to a suitable linearization of a nonlinear problem implies the stability (or instability) of solutions to the original nonlinear problem. In this work, we…
Using molecular dynamics, we study the nucleation and stability of bulk nanobubble clusters. We study the formation, growth, and final size of bulk nanobubbles. We find that, as long as the bubble-bubble interspacing is small enough, bulk…
This paper is concerned with the decentralized stabilization problem for a class of uncertain large-scale systems with Markovian jump parameters. The controllers use local subsystem states and neighboring mode information to generate local…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
Nonlinear isolated and coupled oscillators are extensively studied as prototypical nonlinear dynamics models. Much attention has been devoted to oscillator synchronization or the lack thereof. Here, we study the synchronization and…
Planar wave trains are traveling wave solutions whose wave profiles are periodic in one spatial direction and constant in the transverse direction. In this paper, we investigate the stability of planar wave trains in reaction-diffusion…