相关论文: Critical Transitions and Perturbation Growth Direc…

In the last decade it has been shown that a large class of phase oscillator models admit low dimensional descriptions for the macroscopic system dynamics in the limit of an infinite number N of oscillators. The question of whether the…

Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…

We conjecture that in one-dimensional spatially extended systems the propagation velocity of correlations coincides with a zero of the convective Lyapunov spectrum. This conjecture is successfully tested in three different contexts: (i) a…

Many biological ecosystems exhibit chaotic behavior, demonstrated either analytically using parameter choices in an associated dynamical systems model or empirically through analysis of experimental data. In this paper, we provide a…

The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…

The combination of the compactness of networks, featuring small diameters, and their complex architectures results in a variety of critical effects dramatically different from those in cooperative systems on lattices. In the last few years,…

The sensitivity of trajectories over finite time intervals t to perturbations of the initial conditions can be associated with a finite-time Lyapunov exponent lambda, obtained from the elements M_{ij} of the stability matrix M. For globally…

Early-warning signals of delicate design are always used to predict critical transitions in complex systems, which makes it possible to render the systems far away from the catastrophic state by introducing timely interventions. Traditional…

We show that long chaotic transients dominate the dynamics of randomly diluted networks of pulse-coupled oscillators. This contrasts with the rapid convergence towards limit cycle attractors found in networks of globally coupled units. The…

We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects…

This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…

We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we…

The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos this property is usually quantified by…

The work treats systems combining slow and fast motions depending on each other where fast motions are perturbations of families of either dynamical systems or Markov processes with freezed slow variable. In the first case we consider…

We apply to bidimensional chaotic maps the numerical method proposed by Ginelli et al. to approximate the associated Oseledets splitting, i.e. the set of linear subspaces spanned by the so called covariant Lyapunov vectors (CLV) and…

Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a…

The aim of this research work is to compare the reliability of several variational indicators of chaos on mappings. The Lyapunov Indicator (LI); the Mean Exponential Growth factor of Nearby Orbits (MEGNO); the Smaller Alignment Index…

Recent work has introduced the concept of finite-time scaling to characterize bifurcation diagrams at finite times in deterministic discrete dynamical systems, drawing an analogy with finite-size scaling used to study critical behavior in…

We introduce static and dynamic correlation functions for the spatial densities of Lyapunov vector fluctuations. They enable us to show, for the first time, the existence of hydrodynamic Lyapunov modes in chaotic many-particle systems with…

Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…