Related papers: Will a Large Complex System be Stable? Revisited
In this report, I will review some of the most used models in theoretical ecology along with appealing reformulations and recent results in terms of diversity, stability, and functioning of large well-mixed ecological communities.
Complex networks are ubiquitous: a cell, the human brain, a group of people and the Internet are all examples of interconnected many-body systems characterized by macroscopic properties that cannot be trivially deduced from those of their…
A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…
The effect of rotation upon the classical two-layer Rayleigh-Taylor instability is considered theoretically and compared with previous experimental results. In particular we consider a two-layer system with an axis of rotation that is…
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
This paper considers the problem of robust stability for a class of uncertain quantum systems subject to unknown perturbations in the system Hamiltonian. Some general stability results are given for different classes of perturbations to the…
Over the last two decades, several methods have been proposed for stabilizing the dynamics of biological populations. However, these methods have typically been evaluated using different population dynamics models and in the context of very…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Ecological models traditionally explain stability and coexistence through pairwise interactions among species. These interactions can also involve groups of three or more species, higher-order interactions, which recent theory suggests can…
We propose a minimal model of the dynamics of diversity -- replicator equations with extinction, invasion and mutation. We numerically study the behavior of this simple model and show that it displays completely different behavior from the…
In this paper, we mainly study the robust stability of linear continuous systems with parameter uncertainties, a more general kind of uncertainties for system matrices is considered, i.e., entries of system matrices are rational functions…
We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…
Understanding the conditions of feasibility and stability in ecological systems is a major challenge in theoretical ecology. The seminal work of May in 1972 and recent developments based on the theory of random matrices have shown the…
Cells can often choose among several stably heritable phenotypes. Examples are the expression of genes in eukaryotic cells where long chromosomal regions can adopt persistent and heritable silenced or active states, that may be associated…
This work is concerned with the stability of regime-switching processes under the perturbation of the transition rate matrices. From the viewpoint of application, two kinds of perturbations are studied: the size of the transition rate…
It is generally accepted today that our solar system has undergone a phase during which the orbits of the giant planets became very unstable. In recent years, many studies have identified traces of this event and have provided reasonable…
We investigate the formation of stable ecological networks where many species share the same resource. We show that such stable ecosystem naturally occurs as a result of extinctions. We obtain an analytical relation for the number of…
Uncovering the formation process that reproduces the distinct properties of compact super-Earth exoplanet systems is a major goal of planet formation theory. The most successful model argues that non-resonant systems begin as resonant…