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In the past decade, an intensive study of strong approximation of stochastic differential equations (SDEs) with a drift coefficient that has discontinuities in space has begun. In the majority of these results it is assumed that the drift…

Theoretical results regarding two-dimensional ordinary-differential equations (ODEs) with second-degree polynomial right-hand sides are summarized, with an emphasis on limit cycles, limit cycle bifurcations and multistability. The results…

We prove that a system of locally interacting diffusions carrying discrete masses, subject to an environmental noise and undergoing mass coagulation, converges to a system of Stochastic Partial Differential Equations (SPDEs) with…

A method to describe unresolved processes in meteorological models by physically based stochastic processes (SP) is proposed by the example of an energy budget model (EBM). Contrary to the common approach using additive white noise, a…

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in…

Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…

Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise -- arising from the probabilistic and discrete nature of birth and death processes…

A generic saddle-node bifurcation is proposed to modelize fast transitions of finite amplitude arising in geophysical (and perhaps other) contexts, when they result from the intrinsic dynamics of the system. The fast transition is…

This paper formulates two 3D stochastic differential equations (SDEs) of two microbial populations in a chemostat competing over a single substrate. The two models have two distinct noise sources. One is general noise whereas the other is…

Here we present a simple stochastic threshold model consisting of a deterministic slowly decaying term and a fast stochastic noise term. The process shows a pseudo-resonance, in the sense that for small and large intensities of the noise…

Causal discovery is a data-driven paradigm for analyzing complex systems, while physics-based models, such as ordinary differential equations (ODEs), provide mechanistic structure for real-world dynamical processes. Integrating these…

Many dynamical systems exhibit abrupt transitions or tipping as the control parameter is varied. In scenarios where the parameter is varied continuously, the rate of change of control parameter greatly affects the performance of early…

Dryland vegetation ecosystems are known to be susceptible to critical transitions between alternative stable states when subjected to external forcing. Such transitions are often discussed through the framework of bifurcation theory, but…

A numerical analysis for the fully discrete approximation of an operator Lyapunov equation related to linear SPDEs (stochastic partial differential equations) driven by multiplicative noise is considered. The discretization of the Lyapunov…

Tipping points (TP) are abrupt transitions between metastable states in complex systems, most often described by a bifurcation or crisis of a multistable system induced by a slowly changing control parameter. An avenue for predicting TPs in…

We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…

Effective reinforcement learning (RL) for sepsis treatment depends on learning stable, clinically meaningful state representations from irregular ICU time series. While previous works have explored representation learning for this task, the…

Non-uniform sampling arises when an experimenter does not have full control over the sampling characteristics of the process under investigation. Moreover, it is introduced intentionally in algorithms such as Bayesian optimization and…

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

Stochastic dynamical systems allow modelling of transitions induced by disturbances, in particular from an attracting equilibrium and crossing the stable manifold of a saddle. In the small-noise limit, the probability of such transitions is…