Related papers: Trapping Phenomenon Attenuates Tipping Points for …
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…
Period tripling in driven quantum oscillators reveals unique features absent for linear and parametric drive, but generic for all higher-order resonances. Here, we focus at zero temperature on the relaxation dynamics towards a stationary…
A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the system abruptly changes. For example, such critical…
The appearance of so-called exceptional points in the complex spectra of non-Hermitian systems is often associated with phenomena that contradict our physical intuition. One example of particular interest is the state-exchange process…
Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to…
Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded…
Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful…
Whereas the importance of transient dynamics to the functionality and management of complex systems has been increasingly recognized, most of the studies are based on models. Yet in realistic situations the models are often unknown and what…
For piecewise-smooth ordinary differential equations, the occurrence of a Hopf bifurcation on a switching surface is known as a boundary Hopf bifurcation. Boundary Hopf bifurcations are codimension-two, so occur at points in two-parameter…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…
Many real world systems are at risk of undergoing critical transitions, leading to sudden qualitative and sometimes irreversible regime shifts. The development of early warning signals is recognized as a major challenge. Recent progress…
Across natural and human-made systems, transition points mark sudden changes of order and are thus key to understanding overarching system features. Motivated by recent experimental observations, we here uncover an intriguing class of…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…
We study the dynamics of fluctuations at the critical point for two time-asymmetric version of the Curie-Weiss model for spin systems that, in the macroscopic limit, undergo a Hopf bifurcation. The fluctuations around the macroscopic limit…
A bipartite spin system is proposed for which a fast transfer from one defined state into another exists. For sufficient coupling between the spins, this implements a bit-flipping mechanism which is much faster than that induced by…
Microscopic mechanisms of natural processes are frequently understood in terms of random walk models by analyzing local particle transitions. This is because these models properly account for dynamic processes at the molecular level and…
Phase-locked loops (PLL), Costas loops and other synchronizing circuits are featured by the presence of a nonlinear phase detector, described by a periodic nonlinearity. In general, nonlinearities can cause complex behavior of the system…
The dynamics of supercritical fluids, a state of matter beyond the gas-liquid critical point, changes from diffusive to oscillatory motions at high pressure. This transition is believed to occur across a locus of thermodynamic states called…
Subcritical Turing bifurcations of reaction-diffusion systems in large domains lead to spontaneous onset of well-developed localised patterns via the homoclinic snaking mechanism. This phenomenon is shown to occur naturally when balancing…