Related papers: A note on the dependence on parameters for a nonli…

We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…

We propose a new framework for imposing monotonicity constraints in a Bayesian nonparametric setting based on numerical solutions of stochastic differential equations. We derive a nonparametric model of monotonic functions that allows for…

We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…

An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is…

In this paper, we present a novel framework to synthesize robust strategies for discrete-time nonlinear systems with random disturbances that are unknown, against temporal logic specifications. The proposed framework is data-driven and…

In this paper by exploiting critical point theory, the existence of two distinct nontrivial solutions for a nonlinear algebraic system with a parameter is established. Our goal is achieved by requiring an appropriate behavior of the…

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…

Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…

We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…

There is a renewed interest in the uncertainty principle, reformulated from the information theoretic point of view, called the entropic uncertainty relations. They have been studied for various integrable systems as a function of their…

Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…

A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…

Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…

Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…

Maximal monotonicity is explored as a generalization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The theory is developed for maximal monotone one-port circuits, formed by the series…

We start by defining an approach to non-monotonic probabilistic reasoning in terms of non-monotonic categorical (true-false) reasoning. We identify a type of non-monotonic probabilistic reasoning, akin to default inheritance, that is…

This paper studies the problem of testing whether a function is monotone from a nonparametric Bayesian perspective. Two new families of tests are constructed. The first uses constrained smoothing splines, together with a hierarchical…

Nonlinear filtering is the problem of online estimation of a dynamic hidden variable from incoming data and has vast applications in different fields, ranging from engineering, machine learning, economic science and natural sciences. We…

We investigate the stochastic resonance phenomenon in a physical system based on a tunnel diode. The experimental control parameters are set to allow the control of the frequency and amplitude of the deterministic modulating signal over an…

The method of monotonization of difference schemes is being considered in the paper. The method was earlier proposed by the author for stationary problems. It is investigated in the paper more profoundly. The idea of the method is to build…