Related papers: Lectures on Structural Stability in Dynamics
These lecture notes provide a short review of the status of time dependent backgrounds in String theory, and in particular those that contain space-like singularities. Despite considerable efforts, we do not have yet a full and compelling…
Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…
We review some aspects of moduli in string theory. We argue that one should focus on {\it approximate moduli spaces}, and that there is evidence that such spaces exist non-perturbatively. We ask what it would mean for string theory to…
These notes are a slightly enlarged version of my habilitation thesis, where our research interest and main results in the past few years are summarized. Most of the discussion revolves around complex ordinary differential equations and…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a…
A long-standing controversy in studies of spiral structure has concerned the lifetimes of individual spiral patterns. Much theoretical work has sought quasi-stationary spiral modes while N-body simulations have consistently displayed…
We discuss technical results on learning function approximations using piecewise-linear basis functions, and analyze their stability and convergence using nonlinear contraction theory.
We introduce a simple model to describe the interplay between specific and non-specific interactions. We study the influence of various physical factors on the static and dynamic properties of the specific interactions of our model and show…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
In the present work, we study dark solitons in dynamical lattices with the saturable nonlinearity and compare them with those in lattices with the cubic nonlinearity. This comparison has become especially relevant in light of recent…
Dynamic heterogeneity is now recognised as a central aspect of structural relaxation in disordered materials with slow dynamics, and was the focus of intense research in the last decade. Here we describe how initial, indirect observations…
Traditional methods in educational research often fail to capture the complex and evolving nature of learning processes. This chapter examines the use of complex systems theory in education to address these limitations. The chapter covers…
Parabolic geometric flows have the property of smoothing for short time however, over long time, singularities are typically unavoidable, can be very nasty and may be impossible to classify. The idea of this paper is that, by bringing in…
We show that the dynamical stability under linear perturbations of interacting systems in the hydrodynamic regime follows from the first and the second laws of thermodynamics. Our argument extends to systems with spontaneously or softly…
A brief introduction on the issue of stability in generalized modified gravity is presented and the dynamical system methods are used in the investigation of the stability of spatially flat homogeneous cosmologies within a large class of…
We propose a framework for studying the stability of discrete-event systems modelled as switching max-plus linear systems. In this framework, we propose a set of notions of stability for generic discrete-event systems in the max-plus…
Three subjects are considered here: a self-dual non-critical string that appears in Type IIB superstring theory at points in ${\rm K3}$ moduli space where the Type IIA theory has extended gauge symmetry; a conformal field theory singularity…
A central feature of complex systems is the relevance and entanglement of different levels of description. For instance, the dynamics of ecosystems can be alternatively described in terms of large ecological processes and classes of…