Related papers: Persistence in extended dynamical systems
Recent research on the non-stationary nature of the dynamics of complex systems is reviewed through three specific models. The long time dynamics consists of a slow, decelerating but spasmodic release of generalized intrinsic strain. These…
The spatial logistic model is a system of point entities (particles) in $\mathbb{R}^d$ which reproduce themselves at distant points (dispersal) and die, also due to competition. The states of such systems are probability measures on the…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
We investigate the behavior of the residence times density function for different nonlinear dynamical systems with limit cycle behavior and perturbed parametrically with a colored noise. We present evidence that underlying the stochastic…
We consider a large class of nonlinear diffusive systems with nonlocal coupling. By using a non-perturbative analytical approach we are able to determine the convective and absolute instabilities of all the uniform states of these systems.…
Stochastic dynamical systems arise naturally across nearly all areas of science and engineering. Typically, a dynamical system model is based on some prior knowledge about the underlying dynamics of interest in which probabilistic features…
Enhancement of the predictive power and robustness of nonlinear population dynamics models allows ecologists to make more reliable forecasts about species' long term survival. However, the limited availability of detailed ecological data,…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
The long time dynamics of large particles trapped in two inhomogeneous turbulent shear flows is studied experimentally. Both flows present a common feature, a shear region that separates two colliding circulations, but with different…
We study the spatio-temporal spreading of correlations in an ensemble of spins due to dissipation characterized by short- and long-range spatial profiles. We consider systems initially in an uncorrelated state, and find that correlations…
Two properties of a dynamical system, rigidity and non-recurrence, are examined in detail. The ultimate aim is to characterize the sequences along which these properties do or do not occur for different classes of transformations. The main…
Using techniques of non-autonomous dynamical systems, we completely characterize the persistence properties of an almost periodic Nicholson system in terms of some numerically computable exponents. Although similar results hold for a class…
This article shows how to specify and construct a discrete, stochastic, continuous-time model specifically for ecological systems. The model is more broad than typical chemical kinetics models in two ways. First, using time-dependent hazard…
This work advances the theoretical foundations of reservoir computing (RC) by providing a unified treatment of fading memory and the echo state property (ESP) in both deterministic and stochastic settings. We investigate state-space…
We study the dynamics of density fluctuations in purely diffusive systems away from equilibrium. Under some conditions the static density correlation function becomes long-ranged. We then analyze this behavior in the framework of…
We study the early time dynamics of bimodal spin systems on $2d$ lattices evolving with different microscopic stochastic updates. We treat the ferromagnetic Ising model with locally conserved order parameter (Kawasaki dynamics), the same…
We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations,…
We show that the correlation and entanglement dynamics of spin systems can be understood in terms of propagation of spin waves. This gives a simple, physical explanation of the behaviour seen in a number of recent works, in which a…
In the present work we recall and extend the results of previous work concerning the time evolution of open quantum systems. We show how general properties of such systems are related to their structure properties, those of their…
A method to apply and visualize persistent homology of time series is proposed. The method captures persistent features in space and time, in contrast to the existing procedures, where one usually chooses one while keeping the other fixed.…