Related papers: Universal formats for nonlinear dynamical systems
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
We show that every flat nonlinear discrete-time system with two inputs can be transformed into a structurally flat normal form by state- and input transformations. This normal form has a triangular structure and allows to read off the flat…
A number of recent studies have proposed that linear representations are appropriate for solving nonlinear dynamical systems with quantum computers, which fundamentally act linearly on a wave function in a Hilbert space. Linear…
We consider nonlinear multibody systems and present a suitable set of coordinates for the internal dynamics which allow to decouple the internal dynamics without the need to compute the Byrnes-Isidori form. Furthermore, we derive sufficient…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
The vast majority of systems of practical interest are characterised by nonlinear dynamics. This renders the control and optimization of such systems a complex task due to their nonlinear behaviour. Additionally, standard methods such as…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…
Presenting systems of differential equations in the form of diagrams has become common in certain parts of physics, especially electromagnetism and computational physics. In this work, we aim to put such use of diagrams on a firm…
It is sometimes desirable to produce for a nonlinear system of ODEs a new representation of simpler structural form, but it is well known that this goal may imply an increase in the dimension of the system. This is what happens if in this…
Structure and dynamics of real nanosystems emerge from the unreduced solution of the underlying interaction problem. It has the property of dynamic multivaluedness giving genuine dynamic randomness and complexity (physics/9806002,…
We study the well-posedness of radial solutions for general nonlinear hyperbolic systems in three dimensions. We give a proof of the global existence of radial solutions for general semilinear hyperbolic systems in 3D under null condition,…
We study dissipative dynamics constructed by means of non-commutative Dirichlet forms for various lattice systems with multiparticle interactions associated to CCR algebras. We give a number of explicit examples of such models. Using an…
We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous,…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
The mechanics of the structured particles develops. The substantiation of applicability of such mechanics for the description of processes of evolution in open nonequilibrium systems is offered. The consequences following from the equations…
The method of nonlinear realizations and the technique previously developed in arXiv:1208.1403 are used to construct a dynamical system without higher derivative terms, which holds invariant under the l-conformal Newton-Hooke group. A…
The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass…