Related papers: Stochastic systems with memory and jumps

One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…

We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…

This work proposes a general framework for capturing noise-driven transitions in spatially extended non-equilibrium systems and explains the emergence of coherent patterns beyond the instability onset. The framework relies on stochastic…

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…

In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…

We show that a cumulative action of noise and delayed feedback on an excitable theta-neuron leads to rather coherent stochastic bursting. An idealized point process, valid if the characteristic time scales in the problem are well-separated,…

Stochastic processes with renewal properties are powerful tools for modeling systems where memory effects and long-time correlations play a significant role. In this work, we study a broad class of renewal processes where a variable's value…

We present a computational model of mathematical reasoning according to which mathematics is a fundamentally stochastic process. That is, on our model, whether or not a given formula is deemed a theorem in some axiomatic system is not a…

We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…

In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…

We present simple classical dynamical models to illustrate the idea of introducing a stochasticity with non-locality into the time variable. For stochasticity in time, these models include noise in the time variable but not in the "space"…

Reservoir computing is a form of machine learning that utilizes nonlinear dynamical systems to perform complex tasks in a cost-effective manner when compared to typical neural networks. Many recent advancements in reservoir computing, in…

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…

Continuous-time stochastic systems have attracted a lot of attention recently, due to their wide-spread use in finance for modelling price-dynamics. More recently models taking into accounts shocks have been developed by assuming that the…

Sound is an information-rich medium that captures dynamic physical events. This work presents STReSSD, a framework that uses sound to bridge the simulation-to-reality gap for stochastic dynamics, demonstrated for the canonical case of a…

Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these…

Uncertainties are abundant in complex systems. Mathematical models for these systems thus contain random effects or noises. The models are often in the form of stochastic differential equations, with some parameters to be determined by…

Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of…