Related papers: Fractals in rate-induced tipping
We investigate the geometry of a critical system undergoing a second order thermal phase transition. Using a local description for the dynamics characterizing the system at the critical point T=Tc, we reveal the formation of clusters with…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
Short-time dynamics of many-body systems may exhibit non-analytical behavior of the systems' properties at particular times, thus dubbed dynamical quantum phase transition. Simulations showed that in the presence of disorder new critical…
The current definition of rate-induced tipping is tied to the idea of a pullback attractor limiting in forward and backward time to a stable quasi-static equilibrium. Here we propose a new definition that encompasses the standard definition…
Many models of fractal growth patterns (like Diffusion Limited Aggregation and Dielectric Breakdown Models) combine complex geometry with randomness; this double difficulty is a stumbling block to their elucidation. In this paper we…
If a point particle moves chaotically through a periodic array of scatterers the associated transport coefficients are typically irregular functions under variation of control parameters. For a piecewise linear two-parameter map we analyze…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…
A field theory of frictionless grain packings in two dimensions is shown to exhibit a zero-temperature critical point at a non-zero value of the packing fraction. The zero-temperature constraint of force-balance plays a crucial role in…
There is much interest in the phenomenon of rate-induced tipping, where a system changes abruptly when forcings change faster than some critical rate. Here, we demonstrate and analyse rate-induced tipping in the classic "Daisyworld" model.…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Critical transitions or regime shifts are sudden and unexpected changes in the state of an ecosystem, that are usually associated with dangerous levels of environmental change. However, recent studies show that critical transitions can also…
A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…
We show that a one-dimensional chain of trapped ions can be engineered to produce a quantum mechanical system with discrete scale invariance and fractal-like time dependence. By discrete scale invariance we mean a system that replicates…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…
Active fluids, composed of individual self-propelled agents, can generate complex large-scale coherent flows. A particularly important laboratory realization of such an active fluid is a system composed of microtubules, aligned in a…
We consider the dynamic escape of a small packet of ultracold atoms launched from within an optical dipole trap. Based on a theoretical analysis of the underlying nonlinear dynamics, we predict that fractal behavior can be seen in the…
The transition from static to dynamic friction is often described as a fracture-like instantaneous slip. However, studies on slow sliding processes aimed at understanding frictional instabilities and earthquakes report slow friction…
A tipping point can be defined as an abrupt shift in the properties or behaviour of a system. Tipping points in complex systems from a wide variety of scientific disciplines have been compared to phase transitions in physics, but consistent…
We show how coupling an ensemble of bistable systems to a common cavity field affects the collective stochastic behavior of this ensemble. In particular, the cavity provides an effective interaction between the systems, and parametrically…
In this paper the author presents the results of the preliminary investigation of fractional dynamical systems based on the results of numerical simulations of fractional maps. Fractional maps are equivalent to fractional differential…