相关论文: A sample-paths approach to noise-induced synchroni…
Nonlinear dynamical systems possessing reflection symmetry have an invariant subspace in the phase space. The dynamics within the invariant subspace can be random or chaotic. As a system parameter changes, the motion transverse to the…
A common problem to signal processing are biases introduced by correlated noise. When quantifying time delays between two signals, mixed noise introduces a bias towards zero delay in conventional delay estimates based on the cross- or…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that…
We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial…
We consider the NLS equation with a linear double well potential. Symmetry breaking, i.e., the localisation of an order parameter in one of the potential wells that can occur when the system is symmetric, has been studied extensively.…
We discuss a model for phase transitions in which a double-well potential is singularly perturbed by possibly several terms involving different, arbitrarily high orders of derivation. We study by $\Gamma$-convergence the asymptotic…
An asymmetric double-well potential is considered, assuming that the minima of the wells are quadratic with a frequency $\omega$ and the difference of the minima is close to a multiple of $\hbar \omega$. A WKB wave function is constructed…
We develop a theory of macroscopic resonant tunneling of flux in a double-well potential in the presence of realistic flux noise with significant low-frequency component. The rate of incoherent flux tunneling between the wells exhibits…
We describe synchronization transitions in an ensemble of globally coupled phase oscillators with a bi-harmonic coupling function, and two sources of disorder - diversity of intrinsic oscillatory frequencies and external independent noise.…
The combination of bistability and noise is ubiquitous in complex systems, from biological to social interactions, and has important implications for their functioning and resilience. We analyze a simple three-state model for bistability in…
We study small white noise perturbations of planar dynamical systems with heteroclinic networks in the limit of vanishing noise. We show that the probabilities of transitions between various cells that the network tessellates the plane into…
We investigate coherent and incoherent tunneling phenomena in conditions of crossing diabatic potentials. We consider a model of two crossing parabolic diabatic potentials with an independent of coordinates constant adiabatic coupling. As a…
Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with…
We propose an approximation for the probability of tipping when the speed of parameter change and additive white noise interact to cause tipping. Our approximation is valid for small to moderate drift speeds and helps to estimate the…
The phenomenon of critical slowing down (CSD) has played a key role in the search for reliable precursors of catastrophic regime shifts. This is caused by its presence in a generic class of bifurcating dynamical systems. Simple time-series…
In this work, we analyse the effect of adding Gaussian white noise to the slow variable of a slow--fast system passing through a saddle--node (or fold) bifurcation. This problem is mainly motivated by applications to non-equilibrium energy…
We consider noise-driven exit from a domain of attraction in a two-dimensional bistable system lacking detailed balance. Through analog and digital stochastic simulations, we find a theoretically predicted bifurcation of the most probable…
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 generalize here the one-level consideration in our recent paper arXiv:1901.00411 [1] to the case when an electron collides with a potential that have any number of s bound states. We investigate peculiarities in the Wigner time delay…
It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the…