相关论文: Internal noise interference to warnings of tipping…

There is growing interest in anticipating critical transitions in natural systems, often pursued through statistical detection of early warning signals associated with dynamical bifurcations. In stochastic dynamical systems, such signals…

Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…

Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…

Chemical, physical and ecological systems passing through a saddle-node bifurcation will, momentarily, find themselves balanced at a semi-stable steady state. If perturbed by noise, such systems will escape from the zero-steady state, with…

Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

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…

We employ a typical genetic circuit model to explore how noise can influence the dynamic structure. With the increase of a key interactive parameter, the model will deterministically go through two bifurcations and three dynamic structure…

A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…

We investigate the influence of intrinsic noise on stable states of a one-dimensional dynamical system that shows in its deterministic version a saddle-node bifurcation between monostable and bistable behaviour. The system is a modified…

Previous studies have shown that noise can induce coherence resonance in some nonlinear dynamical systems close to a bifurcation of a periodic motion, such as in excitable systems. We demonstrate that coherence resonance can be observed in…

It has been shown that perturbing the input during training implicitly regularises the gradient of the learnt function, leading to smoother models and enhancing generalisation. However, previous research mostly considered the addition of…

The dynamics of an ensemble of bistable elements with global time-delayed coupling under the influence of noise is studied analytically and numerically. Depending on the noise level the system undergoes ordering transitions and demonstrates…

We study the effects of noise cross-correlations on the steady states of driven, nonequilibrium systems, which are described by two stochastically driven dynamical variables, in one dimension. We use a well-known stochastically driven…

Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering…

Slowing down phenomena occur in both deterministic and stochastic dynamical systems at the vicinity of phase transitions or bifurcations. An example is found in systems exhibiting a saddle-node bifurcation, which undergo a dramatic time…

Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if…

We develop an early-warning signal for bifurcations of one-dimensional random difference equations with additive bounded noise, based on the asymptotic behaviour of the stationary density near a boundary of its support. We demonstrate the…

Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interfere with the linear stability of scalar nonlinear systems when these are subject to time delay. We…

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…

This work investigates a three-dimensional slow-fast stochastic system with quadratic nonlinearity and additive noise, inspired by fluid dynamics. The deterministic counterpart exhibits a periodic orbit and a slow manifold. We demonstrate…