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Consider a dynamical system given by a planar differential equation, which exhibits an unstable periodic orbit surrounding a stable periodic orbit. It is known that under random perturbations, the distribution of locations where the…
We show how the evolution of atoms in a tilted lattice can be changed and controlled by phase noise on the lattice. Dependent on the characteristic parameters of the noise, the interband transport can either be suppressed or enhanced, which…
We study the statistical properties of stochastic evolution equations driven by space-only noise, either additive or multiplicative. While forward problems, such as existence, uniqueness, and regularity of the solution, for such equations…
This paper presents a general theory that aims at explaining timescales observed empirically in technology transitions and predicting those of future transitions. This framework is used further to derive a theory for exploring the dynamics…
We investigate a phase transition from linear to nonlinear information processing in echo state networks, a widely used framework in reservoir computing. The network consists of randomly connected recurrent nodes perturbed by a noise and…
We investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked, overdamped bistable potential driven by white Gaussian noise, the archetype description of Stochastic Resonance. We present a…
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates a class of random dynamical systems, arising from perturbing a one-dimensional piecewise…
We study the disruption process of hierarchical 3-body systems with bodies of comparable mass. Such systems have long survival times that vary by orders of magnitude depending on the initial conditions. By comparing with 3-body numerical…
The predictability problem for systems with different characteristic time scales is investigated. It is shown that even in simple chaotic dynamical systems, the leading Lyapunov exponent is not sufficient to estimate the predictability…
It is a common phenomenon in nature and technology that a system under perturbations exits a regime of its usual dynamics. Often it is possible to define a potential function whereby a potential well can be associated with a usual or…
The influence of noise on the generalized synchronization regime in the chaotic systems with dissipative coupling is considered. If attractors of the drive and response systems have an infinitely large basin of attraction, generalized…
A technique is introduced for estimating unknown parameters when time series of only one variable from a multivariate nonlinear dynamical system is given. The technique employs a combination of two different control methods, a linear…
The propagation of a state vector is governed by a set of time-invariant state transition matrices that switch arbitrarily between two values. The evolution of the state is also perturbed by white Gaussian noise with a variance that…
Dynamical systems driven by a general L\'evy stable noise are considered. The inertia is included and the noise, represented by a generalised Ornstein-Uhlenbeck process, has a finite relaxation time. A general linear problem (the additive…
We address the problem of community detection in networks by introducing a general definition of Markov stability, based on the difference between the probability fluxes of a Markov chain on the network at different time scales. The…
We demonstrate how coupling nonlinear dynamical systems can reduce the effects of noise. For simplicity we investigate noisy coupled map lattices. Noise from different lattice nodes can diffuse across the lattice and lower the noise level…
This paper compiles several aspects of the dynamics of stochastic approximation algorithms with Markov iterate-dependent noise when the iterates are not known to be stable beforehand. We achieve the same by extending the lock-in probability…
We consider a general honest homogeneous continuous-time Markov process with restarts. The process is forced to restart from a given distribution at time moments generated by an independent Poisson process. The motivation to study such…
The sensitivity of a wave field's evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach…