Related papers: On the asymptotic stability of a rational multi-pa…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
The Cahn-Hilliard equation is related with a number of interesting physical phenomena like the spinodal decomposition, phase separation and phase ordering dynamics. On the other hand this equation is very stiff an the difficulty to solve it…
This paper shows nonlinear stability of homogeneous states in second-order hyperbolic systems of partial differential equations that model the dynamics of dissipative relativistic fluids, by checking a dissipativity criterion formulated…
We examine synchronization of identical chaotic systems coupled in a drive/response manner. A rigorous criterion is presented which, if satisfied, guarantees that synchronization to the driving trajectory is linearly stable to…
In this note we show the the system of difference equations $$ x_{n+1}=\dfrac{ay_{n-2}x_{n-1}y_n+bx_{n-1}y_{n-2}+cy_{n-2}+d}{y_{n-2}x_{n-1}y_n},$$ $$y_{n+1}=\dfrac{ax_{n-2}y_{n-1}x_n+by_{n-1}x_{n-2}+cx_{n-2}+d}{x_{n-2}y_{n-1}x_n},$$ where…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
In this paper, incremental exponential asymptotic stability of a class of switched Carath\'{e}odory nonlinear systems is studied based on the novel concept of measure of switched matrices via multiple norms and the transaction coefficients…
Thermalisation of configurations with initial white noise power spectrum is studied in numerical simulations of a classical one-component $\Phi^4$ theory in 2+1 dimensions, coupled to a small amplitude homogenous external field. The study…
In this paper, we establish a necessary and sufficient stability condition for a class of two coupled first-order linear hyperbolic partial differential equations. Through a backstepping transform, the problem is reformulated as a stability…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
Robust Markov Decision Processes (MDPs) are a powerful framework for modeling sequential decision-making problems with model uncertainty. This paper proposes the first first-order framework for solving robust MDPs. Our algorithm interleaves…
We introduce a generalized version of the famous Stable Marriage problem, now based on multi-modal preference lists. The central twist herein is to allow each agent to rank its potentially matching counterparts based on more than one…
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
Let f(t) be a rational function of degree at least 2 with rational coefficients. For a given rational number x_0, define x_{n+1}=f(x_n) for each nonnegative integer n. If this sequence is not eventually periodic, then the difference…
In this review we discuss the persistence and the related first-passage properties in extended many-body nonequilibrium systems. Starting with simple systems with one or few degrees of freedom, such as random walk and random acceleration…
Recent advances in nonlinear dynamical systems theory provide a new insight into numerical properties of discrete algorithms developed to solve nonlinear initial value problems. Basic features like accuracy and stability are well pointed…
Least squares estimator of the stability parameter $\varrho := |\alpha| + |\beta|$ for a spatial unilateral autoregressive process $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\varepsilon_{k,\ell}$ is investigated. Asymptotic…