Related papers: Bifurcations Caused by the Diffusion-Induced Noise

We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics…

We examine the effects of a periodically varying flow velocity on the standing and travelling wave patterns formed by the flow-distributed oscillation (FDO) mechanism. In the kinematic (or diffusionless) limit, the phase fronts undergo a…

Parametric fluctuations or stochastic signals are introduced into the control pulse sequence to investigate the feasibility of random control over quantum open systems. In a large parameter error region, the out-of-order control pulses work…

We consider the behaviour of attractors near invariant subspaces on varying a parameter that does not preserve the dynamics in the invariant subspace but is otherwise generic, in a smooth dynamical system. We refer to such a parameter as…

We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a…

Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…

We investigate the emergence of complex dynamics in a system of coupled dissipative kicked rotors and show that critical transitions can be understood via bifurcations of simple states. We study multistability and bifurcations in the single…

We analyze the noise in a multi-terminal multi-channel conductor under arbitrary time-dependent driving and subject to -- possibly large -- static potential and temperature biases. We show that the full out-of-equilibrium zero-frequency…

We study the inductive biases of diffusion models with a conditioning-variable, which have seen widespread application as both text-conditioned generative image models and observation-conditioned continuous control policies. We observe that…

Diffusion in a multidimensional energy surface with minima and barriers is a problem of importance in statistical mechanics and also has wide applications, such as protein folding. To understand it in such a system, we carry out theory and…

The aim of this work is to study the effect of diffusion on the stability of the equilibria in a general two-components reaction-diffusion system with Neumann boundary conditions in the space of continuous functions. As by product, we…

In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…

The effects of fluctuating boundaries on a superposition state of a quantum particle in a box is studied. We consider a model in one space dimension in which the initial state is a coherent superposition of two energy eigenstates. The…

Varying one of the governing parameters of a dynamical system may lead to a critical transition, where the new stable state is undesirable. In some cases, there is only a limited range of the bifurcation parameter that corresponds to that…

An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…

The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…

We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…

Motion of chemically driven droplets is analyzed by applying a solvability condition of perturbed hydrodynamic equations affected by the adsorbate concentration. Conditions for traveling bifurcation analogous to a similar transition in…

A study was made of the instability that arises when acoustic and gravity waves propagate in an inhomogeneous medium which is characterized by oscillatory approach of the reaction coordinates to the steady state. It is shown that loss of…

We report on experiments addressing the non-linear interaction between a nano-mechanical mode and position fluctuations. The Duffing non-linearity transduces the Brownian motion of the mode, and of other non-linearly coupled ones, into…