相关论文: Dynamical Systems: Some Computational Problems

Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…

In many commercial and academic settings, numerical solvers fail to achieve their theoretical performance levels due to issues in the system definition, parameterization, and even implementation. We propose a pair of methods for detecting…

Bifurcation equations, non-degeneracy and transversality conditions are obtained for the fold, transcritical, pitchfork and flip bifurcations for periodic points of one dimensional implicitly defined discrete dynamical systems. The backward…

In this paper we consider the possibility to use numerical simulations for a computer assisted analysis of integrability of dynamical systems. We formulate a rather general method of recovering the obstruction to integrability for the…

A one - parameter dynamical system is associated to the mathematical problem governing the membrane excitability of a ventricular cardiomyocyte, according to the Luo-Rudy I model. An algorithm used to construct the equilibrium curve is…

Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both…

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…

Stable and unstable manifolds, originating from hyperbolic cycles, fundamentally characterize the behaviour of dynamical systems in chaotic regions. This letter demonstrates that their shifts under perturbation, crucial for chaos control,…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…

We study dynamics and bifurcations of 2-dimensional reversible maps having a symmetric saddle fixed point with an asymmetric pair of nontransversal homoclinic orbits (a symmetric nontransversal homoclinic figure-8). We consider…

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…

Resilience broadly describes a quality of withstanding perturbations. Measures of system resilience have gathered increasing attention across applied disciplines, yet existing metrics often lack computational accessibility and…

In this paper, dynamical systems theory and bifurcation theory are applied to investi- gate the rich dynamical behaviours observed in three simple disease models. The 2- and 3-dimensional models we investigate have arisen in previous…

The interplay between interactions and decoherence in many-body systems is of fundamental importance in quantum physics: Decoherence can degrade correlations, but can also give rise to a variety of rich dynamical and steady-state behaviors.…

In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators.…

Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…

Mathematical modelling allows us to concisely describe fundamental principles in biology. Analysis of models can help to both explain known phenomena, and predict the existence of new, unseen behaviours. Model analysis is often a complex…

We review some properties of dynamical systems with slowly varying parameters, when a parameter is moved through a bifurcation point of the static system. Bifurcations with a single zero eigenvalue may create hysteresis cycles, whose area…

We study local bifurcations of periodic solutions to time-periodic (systems of) integrodifference equations over compact habitats. Such infinite-dimensional discrete dynamical systems arise in theoretical ecology as models to describe the…

We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible…