We argue that transient chaos in deterministic dynamical systems is a major source of noiseinduced chaos. The line of arguments is based on the fractal properties of the dynamical invariant sets responsible for transient chaos, which were not taken into account in previous works. We point out that noise-induced chaos is a weak noise phenomenon since intermediate noise strengths destroy fractali...

We present here a novel method for the classical task of finding and extracting recurring spatiotemporal patterns in recorded spiking activity of neuronal populations. In contrast to previously proposed methods it does not seek to classify exactly recurring patterns, but rather approximate versions possibly differing by a certain number of missed, shifted or excess spikes. We achieve this by fi...

We consider the spatio-temporal patterns of disease spread involving structured populations. We start with a general model framework in population biology and spatial ecology where the individual's spatial movement behaviors depend on its maturation status, and we show how delayed reaction diffusion equations with nonlocal interactions arise naturally. We then consider the impact of this delaye...

A phase space theory for population dynamics in Ecology is presented. This theory applies for a certain class of dynamical systems, that will be calledM-systems, for which a conserved quantity, the M-function, can be defined in phase space. ThisM-function is the generator of time displacements and contains all the dynamical information of the system. In this sense the M-function plays the role ...

Let $G$ be a finite simple graph whose vertices and edges are weighted by two functions. In this paper we shall define and calculate entropy of a dynamical system on weights of the graph $G$, by using the weights of vertices and edges of $G$. We examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. At the end it is shown that, for $rin [0,+infty]$, t...

Evolution is an extreme complex dynamical phenomenon which has to be partitioned into simpler systems for an adequate description. Peter Schuster suggested a partition of evolutionary dynamics into three such subsystems 35]: Population Dynamics Population Support Dynamics Genotype{Phenotype Mapping In this paper we present an adequate description of all three systems and a structural and dynami...

Population neural recordings with long-range temporal structure are often best understood in terms of a common underlying low-dimensional dynamical process. Advances in recording technology provide access to an ever-larger fraction of the population, but the standard computational approaches available to identify the collective dynamics scale poorly with the size of the dataset. We describe a n...

We have numerically investigated the long term dynamical behavior of known Centaurs. This class of objects is thought to constitute the transitional population between the Kuiper Belt and the Jupiter-family comets (JFCs). In our study, we find that this transient population diffuses into the JFCs and other sinks, but (not surprisingly) does not diffuse back into the parameter space representing...

We have used a proper combination of multiband high-resolution HST-WFPC2 and wide-field ground based observations to image the galactic globular cluster NGC 6266 (M62). The extensive photometric data set allows us to determine the center of gravity and to construct the most extended radial profile ever published for this cluster including, for the first time, detailed star counts in the very in...

The time evolution of giant (D > 1 Mpc) lobe-dominated galaxies is analysed on the basis of dynamical evolution of the entire FRII-type population.