Related papers: Recurrence and Stickiness in the Noisy Harper Map

The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…

We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both…

The motion of oscillatory-like nonlinear Hamiltonian systems, driven by a weak noise, is considered. A general method to find regions of stability in the phase space of a randomly-driven system, based on a specific Poincar\'e map, is…

Cyclic dominance of three species is a commonly occurring interaction dynamics, often denoted the rock-paper-scissors (RPS) game. Such type of interactions is known to promote species coexistence. Here, we generalize recent results of…

Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…

Pulsar timing arrays are ensembles of regularly observed millisecond pulsars timed to high precision. Each pulsar in an array could be affected by a suite of noise processes, most of which are astrophysically motivated. Analysing them…

We report an empirical determination of the probability density functions P(r) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 x 5 km^2 and time intervals dt =1, 10, 100 and…

We investigate the behavior of a model neuron that receives a biophysically-realistic noisy post-synaptic current based on uncorrelated spiking activity from a large number of afferents. We show that, with static synapses, such noise can…

Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…

We study the effects of additive noise on the lifetimes of chaotic repellors. Using first order perturbation theory we argue that noise will increase the lifetime if the escape holes lie in regions where the unperturbed density is higher…

Predator-prey models have been shown to exhibit resonance-like behaviour, in which random fluctuations in the number of organisms (demographic noise) are amplified when their frequency is close to the natural oscillatory frequency of the…

Tipping points have been shown to be ubiquitous, both in models and empirically in a range of physical and biological systems. The question of how tipping points cascade through systems has been less well studied and is an important one. A…

Reproducibility of a noisy limit-cycle oscillator driven by a random piecewise constant signal is analyzed. By reducing the model to random phase maps, it is shown that the reproducibility of the limit cycle generally improves when the…

Deep neural networks are extremely successful in various applications, however they exhibit high computational demands and energy consumption. This is exacerbated by stuttering technology scaling, prompting the need for novel approaches to…

We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between…

We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main…

Stochastic fluid dynamics governs the long time tails of hydrodynamic correlation functions, and the critical slowing down of relaxation phenomena in the vicinity of a critical point in the phase diagram. In this work we study the role of…

We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered,…

We analyze the effects of noise on the permutation entropy of dynamical systems. We take as numerical examples the logistic map and the R\"ossler system. Upon varying the noise strengthfaster, we find a transition from an…

The influence of an external random field on the competition process in a nonlinear open spatially extended system is analyzed numerically. A three-component model is chosen as the competition model in which a "weak" species can move in…