Many biological, physical and social systems exhibit correlations in their dynamics across multiple time scales. Such correlations manifest themselves as a broad spectrum of relaxation times and a 1/f decay in the power spectrum, which reflects temporal self-similarity in the dynamics. Such spectra are observed Read more
In statistics and probability theory, a point process is a collection of mathematical points randomly located within a mathematical space such as the real line. In earthquake science, such processes are often used to model the occurrence of earthquake events in time, as stress builds in the Earth’s crust before being released at specific moments.
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Rock–Paper–Scissors is a well-known game, which also offers a simple model of competition between three species or, equivalently, strategies. When modelled in continuous time with ordinary differential equations, this system contains a heteroclinic cycle between the three distinct equilibrium solutions, each representing a steady state with just a single species. Read more
Numerical climate models have long been used in the study of the Earth’s palaeoclimate – the climate in ancient times before modern instrumental records. Examples range from early investigations based on simple thermodynamic or general circulation models to the modern state-of-the-art models now being used in the Paleoclimate Modelling Intercomparison Project. Read more
Researchers and policymakers tasked with planning for climate change often turn to so-called integrated assessment models (IAMs) to examine possible scenarios for Earth futures under different policy options. Read more
The structure of a complex network influences any dynamical processes occurring within it. In particular, strong heterogeneities in network structure often underlie nontrivial dynamical properties of networked systems. Read more
Seismic monitoring plays a fundamental role in mitigating hazards near volcanoes, where thousands of earthquakes can occur each day during periods of unrest. These events produce a diverse range of seismic signals, and the detection of the initial primary (P-) and secondary/shear (S-) wave arrivals forms the basis of most seismic processing tasks undertaken to determine earthquake locations, magnitudes and source parameters. Read more
The effect an individual node or edge can have on a network’s structure and dynamics depends not only on the scale of its activity, but also on its position within the network, as well as the activity of neighbouring nodes and edges. Read more
Since its first formulation in 1964, the so-called “big jump principle” (BJP) of extreme value statistics has played an important role in fields such as large deviation theory and financial mathematics. For heavy-tailed distributions, the principle considers N independent and identically distributed (IID) random variables, and links the statistics of the sum of these variables and of their maximum value. Read more
For more than half a century, researchers have employed mathematical models to better understand the response of the Earth’s climate to internal fluctuations as well as external perturbations, whether anthropogenic or solar. These models range from highly complex and multi-dimensional general circulation models to simplified energy balance models. Read more
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