Related papers: Non linear system become linear system

In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…

This text aims at providing a bird's eye view of system identification with special attention to nonlinear systems. The driving force is to give a feeling for the philosophical problems facing those that build mathematical models from data.…

The paper studies the relation between a nonlinear time-varying flat discrete-time system and the corresponding linear time-varying systems which are obtained by a linearization along trajectories. It is motivated by the continuous-time…

Here we give a complete group classification of the general case of linear systems of three second-order ordinary differential equations excluding the case of systems which are studied in the literature. This is given as the initial step in…

Presented is a new method yielding parameterized solution to an interval parametric linear system. Some properties of this method are discussed. The solution enclosure it provides is compared to the enclosures by other methods. It is shown…

We study a material modeled as a network of nodes connected by edges. Using a discrete approach, we build a nonlinear algebraic system that connects applied forces to internal forces and node positions. The model can describe elasticity,…

Interconnected dynamic systems are a pervasive component of our modern infrastructures. The complexity of such systems can be staggering, which motivates simplified representations for their manipulation and analysis. This work introduces…

Linear oscillators contribute to most branches of contemporary quantum science. They have already successfully served as quantum sensors and memories, found applications in quantum communication, and hold promise for cluster-state-based…

We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…

In this paper, we derive a framework to understand the effect of imperfections on the phasematching spectrum of a wide class of nonlinear systems. We show that this framework is applicable to many physical systems, such as waveguides or…

The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…

The paper intends to offer a general overview on what the concept of integrability means for a nonlinear dynamical system and how the symmetry method can be applied for approaching it. After a general part where key problems as direct and…

With new advances in machine learning and in particular powerful learning libraries, we illustrate some of the new possibilities they enable in terms of nonlinear system identification. For a large class of hybrid systems, we explain how…

Nonlinear response theory, in contrast to linear cases, involves (dynamical) details, and this makes application to many body systems challenging. From the microscopic starting point we obtain an exact response theory for a small number of…

To understand large, connected systems, we cannot only zoom into the details. We also need to see the large-scale features from afar. One way to take a step back and get the whole picture is to model the systems as a network. However, many…

Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…

The problems and solutions contained here, all associated with nonlinear recurrences and long-term trends, are new (as far as is known).

We give a unified approach to various results and problems of nonclassical logics

Individual choices often depend on the order in which the decisions are made. In this paper, we expose a general theory of measurable systems (an example of which is an individual's preferences) allowing for incompatible (non-commuting)…

The paper describes a system of rays declining at small angles in lasers. The correlation between a group of rays and binomial coefficients is shown. The correlation of distribution of rays in the system of numbers placed in a…