Chaos and Predictability in Ionospheric Time Series.

Modelling the Earth's ionosphere is a big challenge, due to the complexity of the system. Different first principle models have been developed over the last 50 years, based on ionospheric physics and chemistry, mostly controlled by Space Weather conditions. However, it is not understood in depth if the residual or mismodelled component of the ionosphere's behaviour is predictable in principle as a simple dynamical system, or is conversely so chaotic to be practically stochastic. Working on an ionospheric quantity very popular in aeronomy, we here suggest data analysis techniques to deal with the question of how chaotic and how predictable the local ionosphere's behaviour is. In particular, we calculate the correlation dimension D2 and the Kolmogorov entropy rate K2 for two one-year long time series of data of vertical total electron content (vTEC), collected on the top of the mid-latitude GNSS station of Matera (Italy), one for the year of Solar Maximum 2001 and one for the year of Solar Minimum 2008. The quantity D2 is a proxy of the degree of chaos and dynamical complexity. K2 measures the speed of destruction of the time-shifted self-mutual information of the signal, so that K2-1 is a sort of maximum time horizon for predictability. The analysis of the D2 and K2 for the vTEC time series allows to give a measure of chaos and predictability of the Earth's ionosphere, expected to limit any claim of prediction capacity of any model. The results reported here are preliminary, and must be intended only to demonstrate how the application of the analysis of these quantities to the ionospheric variability is feasible, and with a reasonable output.

Metriplectic Structure of a Radiation-Matter-Interaction Toy Model.

A dynamical system defined by a metriplectic structure is a dissipative model characterized by a specific pair of tensors, which defines a Leibniz bracket; and a free energy, formed by a "Hamiltonian" and an entropy, playing the role of dynamics generator. Generally, these tensors are a Poisson bracket tensor, describing the Hamiltonian part of the dynamics, and a symmetric metric tensor, that models purely dissipative dynamics. In this paper, the metriplectic system describing a simplified two-photon absorption by a two-level atom is disclosed. The Hamiltonian component is sufficient to describe the free electromagnetic radiation. The metric component encodes the radiation-matter coupling, driving the system to an asymptotically stable state in which the excited level of the atom is populated due to absorption, and the radiation has disappeared. First, a description of the system is used, based on the real-imaginary decomposition of the electromagnetic field phasor; then, the whole metriplectic system is re-written in terms of the phase-amplitude pair, named Madelung variables. This work is intended as a first result to pave the way for applying the metriplectic formalism to many other irreversible processes in nonlinear optics.

A mathematical model of lithosphere-atmosphere coupling for seismic events.

Significant evidence of ionosphere disturbance in connection to intense seismic events have been detected since two decades. It is generally believed that the energy transfer can be due to Acoustic Gravity Waves (AGW) excited at ground level by the earthquakes. In spite of the statistical evidence of the detected perturbations, the coupling between lithosphere and atmosphere has not been so far properly explained by an accurate enough model. In this paper, for the first time, we show the result of an analytical-quantitative model that describes how the pressure and density disturbance is generated in the lower atmosphere by the ground motion associated to earthquakes. The direct comparison between observed and modelled vertical profiles of the atmospheric temperature shows the capability of the model to accurately reproduce, with an high statistical significance, the observed temperature fluctuations induced by strong earthquakes.

Steering complex networks toward desired dynamics.

We consider networks of dynamical units that evolve in time according to different laws, and are coupled to each other in highly irregular ways. Studying how to steer the dynamics of such systems towards a desired evolution is of great practical interest in many areas of science, as well as providing insight into the interplay between network structure and dynamical behavior. We propose a pinning protocol for imposing specific dynamic evolutions compatible with the equations of motion on a networked system. The method does not impose any restrictions on the local dynamics, which may vary from node to node, nor on the interactions between nodes, which may adopt in principle any nonlinear mathematical form and be represented by weighted, directed or undirected links. We first explore our method on small synthetic networks of chaotic oscillators, which allows us to unveil a correlation between the ordered sequence of pinned nodes and their topological influence in the network. We then consider a 12-species trophic web network, which is a model of a mammalian food web. By pinning a relatively small number of species, one can make the system abandon its spontaneous evolution from its (typically uncontrolled) initial state towards a target dynamics, or periodically control it so as to make the populations evolve within stipulated bounds. The relevance of these findings for environment management and conservation is discussed.

New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms.

Algorithms based on Empirical Mode Decomposition (EMD) and Iterative Filtering (IF) are largely implemented for representing a signal as superposition of simpler well-behaved components called Intrinsic Mode Functions (IMFs). Although they are more suitable than traditional methods for the analysis of nonlinear and nonstationary signals, they could be easily misused if their known limitations, together with the assumptions they rely on, are not carefully considered. In this work, we examine the main pitfalls and provide caveats for the proper use of the EMD- and IF-based algorithms. Specifically, we address the problems related to boundary errors, to the presence of spikes or jumps in the signal and to the decomposition of highly-stochastic signals. The consequences of an improper usage of these techniques are discussed and clarified also by analysing real data and performing numerical simulations. Finally, we provide the reader with the best practices to maximize the quality and meaningfulness of the decomposition produced by these techniques. In particular, a technique for the extension of signal to reduce the boundary effects is proposed; a careful handling of spikes and jumps in the signal is suggested; the concept of multi-scale statistical analysis is presented to treat highly stochastic signals.

A stretched logistic equation for pandemic spreading.

In this brief work we present a novel approach to the logistic dynamics of populations and epidemic spreading that can take into account of the complex nature of such a process in several real situations, where due to different agents the dynamics is no longer characterized by a single characteristic timescale, but conversely by a distribution of time scales, rendered via a time-dependent growth rate. In detail, a differential equation containing a power-law time dependent growth rate is proposed, whose solution, named Stretched Logistic Function, provides a modified version of the usual logistic function. The model equation is inspired by and applied to the recent spreading on COVID-19 disease in Italy, showing how the real dynamics of infection spreading is characterized by a time dependent dynamics. A speculative discussion of the Stretched Logistic Function in relation to diffusion processes is attempted.

Kleptoparasitism and Scavenging Can Stabilize Ecosystem Dynamics.

Scavenging is ubiquitous in nature, but its implications have rarely been investigated. We used camera traps on wolf kills to investigate the role of scavenging on predator and multiprey dynamics in a northern Apennine system in Italy. In contrast to North American systems, the omnivorous wild boar successfully competes with wolves for the meat of their kills. We developed a deterministic, multitrophic web model (wolf, vegetation, deer, and wild boar), tunable through a parameter that governs the impact of prey sharing between wolves and wild boar. When prey sharing is scarce, populations oscillate, but above a threshold value the trophic web is stabilized, with the regime solution becoming a fixed, stable point. Both deer and wild boar then increase as a function of prey sharing, and the impact of herbivores on the vegetation increases. When prey sharing exceeds another threshold, the system collapses due to the extinction of both wolves and wild boar. Our analysis shows that scavenging is crucial for the dynamics of this ecosystem, and thus it should not be overlooked in food web modeling. The exploitation of wolf kills by wild boar may allow juveniles and yearlings to obtain high-quality resources that are not usually available, helping the wild boar to compensate for losses caused by hunting. This is likely to make them even more invasive and difficult to control.

Magnetic reconnection rate in space plasmas: a fractal approach.

Magnetic reconnection is generally discussed via a fluid description. Here, we evaluate the reconnection rate assuming a fractal topology of the reconnection region. The central idea is that the fluid hypothesis may be violated at the scales where reconnection takes place. The reconnection rate, expressed as the Alfvén Mach number of the plasma moving toward the diffusion region, is shown to depend on the fractal dimension and on the sizes of the reconnection or diffusion region. This mechanism is more efficient than prediction of the Sweet-Parker model and even Petschek's model for finite magnetic Reynolds number. A good agreement also with rates given by Hall MHD models is found. A discussion of the fractal assumption on the diffusion region in terms of current microstructures is proposed. The comparison with in-situ satellite observations suggests the reconnection region to be a filamentary domain.