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Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
Using direct numerical simulations we study dynamo action under the Taylor-Green forcing with Prandtl number less than one. We observe bistability with a weak magnetic field branch and a strong magnetic field branch. Both the dynamo…
The breaking of detailed balance, the symmetry between forward and backward probability transition between two states, is crucial to understand irreversible systems. In hydrodynamic turbulence, a far-from equilibrium system, we observe a…
Many elastic structures exhibit rapid shape transitions between two possible equilibrium states: umbrellas become inverted in strong wind and hopper popper toys jump when turned inside-out. This snap-through is a general motif for the…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
We use importance sampling in a redefined way to highlight and investigate rare events in the form of trajectories trapped inside a target coherent set. We take a transfer operator approach to finding these sets on a reconstructed…
The MHD flow driven by a travelling magnetic field (TMF) in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the system…
Dynamical phase transitions (DPTs) in the space of trajectories are one of the most intriguing phenomena of nonequilibrium physics, but their nature in realistic high-dimensional systems remains puzzling. Here we observe for the first time…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
Linearly stable shear flows first transition to turbulence in the form of localised patches. At low Reynolds numbers, these turbulent patches tend to suddenly decay, following a memoryless process typical of rare events. How far in advance…
We have studied the rich dynamics of a damped particle inside an external double-well potential under the influence of state-dependent time-delayed feedback. In certain regions of the parameter space, we observe multistability with the…
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…
We analyze the probability distribution for entropy production rates of trajectories evolving on a class of out-of-equilibrium kinetic networks. These networks can serve as simple models for driven dynamical systems, which are of particular…
Active matter represents a broad class of systems that evolve far from equilibrium due to the local injection of energy. Like their passive analogues, transformations between distinct metastable states in active matter proceed through rare…
When parameters of a dynamical system change sufficiently fast, critical transitions can take place even in the absence of bifurcations. This phenomenon is known as rate-induced tipping and has been reported in a variety of systems, from…
A pure and incompressible material is confined between two plates such that it is heated from below and cooled from above. When its melting temperature is comprised between these two imposed temperatures, an interface separating liquid and…
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 interaction of a suspension of rotating colloids with a periodically patterned structure is here investigated by means of continuum theoretical predictions and hydrodynamic simulations. Close to the obstacle surface, rotors circulate…
In incompressible and periodic statistically stationary turbulence, exchanges of turbulent energy across scales and space are characterised by very intense and intermittent spatio-temporal fluctuations around zero of the time-derivative…
Bistability of nonlinear resonantly driven oscillator in the presence of external noise is analyzed by means of classical Fokker-Planck equation in quasienergy space with account for tunneling effects and by quantum master equation in…