Related papers: Phase reduction of reaction-diffusion systems with…
We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses…
We propose the deterministic rate equation of three-species in the reaction - diffusion system. For this case, our purpose is to carry out the decay process in our three-species reaction-diffusion model of the form $A+B+C\to D$. The…
In this paper, we first propose a method that can efficiently compute the maximal robust controlled invariant set for discrete-time linear systems with pure delay in input. The key to this method is to construct an auxiliary linear system…
We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an Ordinary Differential Equation, and is inspired by…
We investigate phase diffusion of a two-component Bose-Einstein condensates prepared initially in arbitrary coherent spin state $|\theta_0,\phi_0\rangle$. Analytical expression of the phase-diffusion time is presented for…
Self-assembly processes in biological and synthetic biomolecular systems are often governed by the spatial separation of biochemical processes. While previous work has focused on optimizing self-assembly through fine-tuned reaction…
We introduce a minimization formulation for the determination of a finite-dimensional, time-dependent, orthonormal basis that captures directions of the phase space associated with transient instabilities. While these instabilities have…
We have implemented the gedanken experiment of an individual atom scattering a wave packet of near-resonant light, and measured the associated Wigner time-delay as a function of the frequency of the light. In our apparatus the atom behaves…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…
In this paper, we discuss the feedback stabilization of bilinear systems under weak observation properties. In this case, the uniform stability is not guaranteed. Thus we provide an explicit weak decay rate for all regular initial data.…
We expand on a previous study of fronts in finite particle number reaction-diffusion systems in the presence of a reaction rate gradient in the direction of the front motion. We study the system via reaction-diffusion equations, using the…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
The recent development of compressed sensing has led to spectacular advances in the understanding of sparse linear estimation problems as well as in algorithms to solve them. It has also triggered a new wave of developments in the related…
We present an acceleration method for sequences of large-scale linear systems, such as the ones arising from the numerical solution of time-dependent partial differential equations coupled with algebraic constraints. We discuss different…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
We consider in this paper a reaction-diffusion system under a KPP hypothesis in a cylindrical domain in the presence of a shear flow. Such systems arise in predator-prey models as well as in combustion models with heat losses. Similarly to…
The reflection and transmission of a few-cycle laser pulse impinging on two parallel thin metal layers have been analyzed. The two layers, with a thickness much smaller than the skin depth of the incoming radiation field, are represented by…
In-phase synchronization is a special case of synchronous behavior when coupled oscillators have the same phases for any time moments. Such behavior appears naturally for nearly identical coupled limit-cycle oscillators when the coupling…
The differential equations involving two discrete delays are helpful in modeling two different processes in one model. We provide the stability and bifurcation analysis in the fractional order delay differential equation $D^\alpha x(t)=a…
We investigate the convergence of spatial discretizations for reaction-diffusion systems with mass-action law satisfying a detailed balance condition. Considering systems on the d-dimensional torus, we construct appropriate space-discrete…