Related papers: Noise Induced Pattern Switching in Randomly Distri…
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…
It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are…
In this paper, we study the phase transition behavior emerging from the interactions among multiple agents in the presence of noise. We propose a simple discrete-time model in which a group of non-mobile agents form either a fixed connected…
Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems, specifically, has garnered considerable interest from researchers and developers…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socio-economic changes and climate transitions between ice-ages and warm-ages. From bifurcation…
A time-delayed response of individual living organisms to information exchanged within flocks or swarms leads to the emergence of complex collective behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9 3864),…
Noise is usually regarded as adversarial to extract the effective dynamics from time series, such that the conventional data-driven approaches usually aim at learning the dynamics by mitigating the noisy effect. However, noise can have a…
The time-dependent barrier passage of a particle driven by the structured noise is studied in the field of a metastable potential. Quantities such as the probability of passing over the saddle point and transmission coefficient of the…
It is well known that the addition of noise to a multistable dynamical system can induce random transitions from one stable state to another. For low noise, the times between transitions have an exponential tail and Kramers' formula gives…
Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales,…
By introducing extrinsic noise as well as intrinsic uncertainty into a network with stochastic events, this paper studies the dynamics of the resulting Markov random network and characterizes a novel phenomenon of intermittent…
The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…
We study the effects of time-varying environmental noise on nonequilibrium phase transitions in spreading and growth processes. Using the examples of the logistic evolution equation as well as the contact process, we show that such temporal…
We present a picture of phase transitions of the system with colored multiplicative noise. Considering the noise amplitude as the power-law dependence of the stochastic variable $x^a$ we show the way to phase transitions disorder-order and…
Critical transitions are of great interest to scientists in many fields. Most knowledge about these transitions comes from systems exhibiting the multistability of spatially uniform states. In spatially extended and, particularly, in…