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A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes…
Non-reciprocal systems have been shown to sustain time-dependent patterns, most prominently travelling waves. The transition into these time-dependent states generally breaks time-translational invariance, representing a clear deviation…
Earthquake cycles are studied by taking into account the interactions among slip, fluid pressure, temperature, and porosity on the fault planes, which are known to play a crucial role in earthquake dynamics. The spring-block model with a…
The phase transitions and critical properties of two types of inhomogeneous systems are reviewed. In one case, the local critical behaviour results from the particular shape of the system. Here scale-invariant forms like wedges or cones are…
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches:…
I study a recently proposed statistical model of earthquake dynamics that incorporates aging as a fundamental ingredient. The model is known to generate earthquake sequences that quantitatively reproduce the spatial and temporal clustering…
Noise-induced phase transitions are common in various complex systems, from physics to biology. In this article, we investigate the emergence of crucial events in noise-induced phase transition processes and their potential significance for…
The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the…
Short and long range interactions between earthquakes are attracting increasing interest. Scale invariant properties of seismicity in time, space and energy argue for the presence of complex triggering mechanisms where, like a cascade…
Seeing the Earth crust as crisscrossed by faults filled with fluid at close to lithostatic pressures, we develop a model in which its elastic modulii are different in net tension versus compression. In constrast with standard nonlinear…
Earthquakes are complex physical processes driven by the stick-slip motion of a sliding fault. After the main quake, a series of aftershocks typically follows. These are loosely defined as events that follow a given event and occur within…
Catastrophes of all kinds can be roughly defined as short duration-large amplitude events following and followed by long periods of "ripening". Major earthquakes surely belong to the class of 'catastrophic' events. Because of the space-time…
Seismicity and faulting within the Earth crust are characterized by many scaling laws that are usually interpreted as qualifying the existence of underlying physical mechanisms associated with some kind of criticality in the sense of phase…
The collapse of man-made and natural structures is a complex phenomenon that has been studied for centuries. We propose a new approach to understanding catastrophic instabilities, based on the idea that they do not occur at the critical…
Out of equilibrium, the lack of reciprocity is the rule rather than the exception. Non-reciprocal interactions occur, for instance, in networks of neurons, directional growth of interfaces, and synthetic active materials. While wave…
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…
We investigate the influence of nonstationary 1/f^mu noise, produced by interacting defects, on a quantum two-level system. Adopting a simple phenomenological model for this noise we describe exactly the corresponding dephasing in various…
Laboratory earthquakes exhibit characteristics of a low dimensional random attractor with a dimension similar to that of natural slow earthquakes. A model of stochastic differential equations based on rate and state-dependent friction…
We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent $\alpha$, which can be experimentally realized in ion traps. We focus on two classes of emergent…
The steady state shock formation in processes like nonconserving asymmetric simple exclusion processes in varied situations is shown to be a nonequilibrium critical phenomenon. The diverging length scales and the quantitative description of…