Related papers: Cusp bifurcations: numerical detection via two-par…
We study the nonlocal Kuramoto-Sivashinsky equation on the one-dimensional torus, \[ u_t+u u_x=\Lambda^{r}u-\varepsilon \Lambda^{s}u,\qquad x\in\mathbb T, \] where $\varepsilon>0$, $s>1$, $r\in[-1,s)$. We first prove local and global…
We revisit a problem considered by Chow and Hale on the existence of subharmonic solutions for perturbed systems. In the analytic setting, under more general (weaker) conditions, we prove their results on the existence of bifurcation curves…
We propose a general framework for computer-assisted verification of the presence of symmetry breaking, period-tupling and touch-and-go bifurcations of symmetric periodic orbits for reversible maps. The framework is then adopted to…
We discuss the occurrence of Poincar\'e-Andronov-Hopf bifurcations in parameter dependent ordinary differential equations, with no a priori assumptions on special coordinates. The first problem is to determine critical parameter values from…
A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used…
This paper presents a stochastic block-coordinate proximal Newton method for minimizing the sum of a blockwise Lipschitz-continuously differentiable function and a separable nonsmooth convex function. At each iteration, the method randomly…
Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work, we develop conservative, positivity-preserving, energy…
In this paper, we present an efficient semismooth Newton method, named SSNCP, for solving a class of semidefinite programming problems. Our approach is rooted in an equivalent semismooth system derived from the saddle point problem induced…
A numerical algorithm is proposed to explore in a systematic way the trajectories of the eigenvalues of non-Hermitian matrices in the parametric space and exploit this in order to find the locations of defective eigenvalues in the complex…
We introduce a cutting-plane framework for nonconvex quadratic programs (QPs) that progressively tightens convex relaxations. Our approach leverages the doubly nonnegative (DNN) relaxation to compute strong lower bounds and generate…
We consider a class of structured fractional minimization problems, in which the numerator part of the objective is the sum of a differentiable convex function and a convex non-smooth function, while the denominator part is a convex or…
Change in the coefficients or in the mean of the innovation distribution of an INAR(p) process is a sign of disturbance that is important to detect. The methods of this paper can test for change in any one of these quantities separately, or…
The direct or algorithmic approach for the Jacobian problem, consisting of the direct construction of the inverse polynomials is proposed. The so called principle and derived Jacobi conditions are proposed and discussed. The algorithmic…
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for…
In this paper we introduce universal asymptotic unfolding normal forms for nonlinear singular systems. Next, we propose an approach to find the parameters of a parametric singular system that they play the role of universal unfolding…
Existing tools for bifurcation detection from signals of dynamical systems typically are either limited to a special class of systems, or they require carefully chosen input parameters, and significant expertise to interpret the results.…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
The Douglas-Rachford splitting algorithm is a classical optimization method that has found many applications. When specialized to two normal cone operators, it yields an algorithm for finding a point in the intersection of two convex sets.…
In the last three decades, powerful computer-assisted techniques have been developed in order to validate a posteriori numerical solutions of semilinear elliptic problems of the form $\Delta u +f(u,\nabla u) = 0$. By studying a well chosen…
We present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment. In particular, we show how the odd-number limitation inherent in popular non-invasive control schemes, such as…