相关论文: Studying discrete dynamical systems trough differe…

This paper is concerned with probabilistic techniques for forecasting dynamical systems described by partial differential equations (such as, for example, the Navier-Stokes equations). In particular, it is investigating and comparing…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable…

A typical system of k difference (or differential) equations can be compressed, or folded into a difference (or ordinary differential) equation of order k. Such foldings appear in control theory as the canonical forms of the controllability…

Let $\Phi:\{0,1\}^{n}\longrightarrow\{0,1\}^{n}$. The asynchronous flows are (discrete time and real time) functions that result by iterating the coordinates $\Phi_{i}$ independently on each other. The purpose of the paper is that of…

We derive a system with one degree of freedom that models a class of dynamical systems with strange attractors in three dimensions. This system retains all the characteristics of chaotic attractors and is expressed by a second-order…

The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…

In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…

We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that certain class of autonomous dynamical systems can generate random dynamics. This dynamics…

In this paper we report a few examples of algebraically solvable dynamical systems characterized by 2 coupled Ordinary Differential Equations which read as follows: x_n = P(n) (x1, x2) , n = 1, 2 , with P(n) (x1, x2) specific polynomials of…

In the study of discrete dynamical systems, we typically start with a function from a space into itself, and ask questions about the properties of sequences of iterates of the function. In this paper we reverse the direction of this study.…

We continue previous work to count non-equivalent dynamical systems over finite fields generated by polynomials or rational functions.

Stochastic differential equations (SDEs) describe dynamical systems where deterministic flows, governed by a drift function, are superimposed with random fluctuations, dictated by a diffusion function. The accurate estimation (or discovery)…

Non-equilibrium self-organized patterns formed by particles interacting through competing range interaction are driven over a substrate by an external force. We show that, with increasing driving force, the pre-existed static patterns…

The flow is very useful in studying dynamical systems. However, many modern systems--notably differential inclusions--do not have unique solutions, and therefore cannot be described by flows. Richard McGehee has proposed an object, the…

In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…

We study the dynamical large deviations (LD) of a class of one-dimensional kinetically constrained models whose (tilted) generators can be mapped into themselves via duality transformations. We consider four representative models in detail:…

We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…