Related papers: Routes to extreme events in dynamical systems: Dyn…

We uncover a route from low-dimensional to high-dimensional chaos in nonsmooth dynamical systems as a bifurcation parameter is continuously varied. The striking feature is the existence of a finite parameter interval of periodic attractors…

Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…

A central problem in uncertainty quantification is how to characterize the impact that our incomplete knowledge about models has on the predictions we make from them. This question naturally lends itself to a probabilistic formulation, by…

Large-scale instabilities occurring in the presence of small-scale turbulent fluctuations are frequently observed in geophysical or astrophysical contexts but are difficult to reproduce in the laboratory. Using extensive numerical…

Bursty dynamics is a common temporal property of various complex systems in Nature but it also characterises the dynamics of human actions and interactions. At the phenomenological level it is a feature of all systems that evolve…

Large language model-powered multi-agent systems have emerged as powerful tools for simulating complex human-like systems. The interactions within these systems often lead to extreme events whose origins remain obscured by the black box of…

We study the coarsening dynamics of a two dimensional system via lattice Boltzmann numerical simulations. The system under consideration is a biphasic system consisting of domains of a dispersed phase closely packed together in a continuous…

Many dynamical systems operate in a fluctuating environment. However, even in low-dimensional setups, transitions and bifurcations have not yet been fully understood. In this Letter we focus on crises, a sudden flooding of the phase space…

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…

A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…

We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…

Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…

Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of…

We introduce a family of area-preserving maps representing a (non-trivial) two-dimensional extension of the Pomeau-Manneville family in one dimension. We analyze the long-time behavior of recurrence time distributions and correlations,…

We use numerical simulations to study the dynamics of dense assemblies of self-propelled particles in the limit of extremely large, but finite, persistence times. In this limit, the system evolves intermittently between mechanical…

We provide an analytic, microscopic analysis of extreme events in an adaptive population comprising competing agents (e.g. species, cells, traders, data-packets). Such large changes tend to dictate the long-term dynamical behaviour of many…

Sudden transitions in the state of a system are often undesirable in natural and human-made systems. Such transitions under fast variation of system parameters are called rate-induced tipping. We experimentally demonstrate rate-induced…

General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal…

Dynamical chaos is a fundamental manifestation of gravity in astrophysical, many-body systems. The spectrum of Lyapunov exponents quantifies the associated exponential response to small perturbations. Analytical derivations of these…

Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…