Related papers: A noise-controlled dynamic bifurcation
We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes depending on how fast the intensity of the noise goes to…
How can precise control be realised in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way to achieve precise control in signal-dependent noisy environments. When the control signal has Poisson…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
Noise-induced transitions between multistable states happen in a multitude of systems, such as species extinction in biology, protein folding, or tipping points in climate science. Large deviation theory is the rigorous language to describe…
We study a two-dimensional low-dissipation dynamical system with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system…
In this work we analyze the stochastic dynamics of the Kauffman model evolving under the influence of noise. By considering the average crossing time between two distinct trajectories, we show that different Kauffman models exhibit a…
It is shown that a well-known theory of random stationary processes contain contradictions. Integral representations of correlation functions and random stationary processes are investigated further. The new method of struggle with…
We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in…
Many physical and biological systems exhibit intrinsic cyclic dynamics that are altered by random external perturbations. We examine continuous-time autonomous dynamical systems exhibiting a stable limit cycle, perturbed by additive…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
Anticipating bifurcation-induced transitions in dynamical systems has gained relevance in various fields of the natural, social, and economic sciences. Before the annihilation of a system's equilibrium point by means of a bifurcation, the…
The effect of weak multiplicative colored noise on the dynamics of a Hamiltonian system is studied by means of asymptotic methods, in the vicinity of homoclinic or heteroclinic trajectories. A general expression for the probability of…
Stop-and-go waves are commonly observed in traffic and pedestrian flows. In traffic theory they are described by phase transitions of metastable models. The self-organization phenomenon occurs due to inertia mechanisms but requires fine…
This work addresses stochastic optimal control problems where the unknown state evolves in continuous time while partial, noisy, and possibly controllable measurements are only available in discrete time. We develop a framework for…
Random fluctuations caused by environmental noise can lead to decoherence in quantum systems. Exploring and controlling such dissipative processes is both fundamentally intriguing and essential for harnessing quantum systems to gain…
We explore the properties of discrete-time stochastic processes with a bounded state space, whose deterministic limit is given by a map of the unit interval. We find that, in the mesoscopic description of the system, the large jumps between…
We analyze the dynamics of the forced singularly perturbed differential equation of Duffing's type. We explain the appearance of the large frequency nonlinear oscillations of the solutions. It is shown that the frequency can be controlled…
Dynamics of a system that performs a large fluctuation to a given state is essentially deterministic: the distribution of fluctuational paths peaks sharply at a certain optimal path along which the system is most likely to move. For the…
We present here a new approach of the partial control method, which is a useful control technique applied to transient chaotic dynamics affected by a bounded noise. Usually we want to avoid the escape of these chaotic transients outside a…