Related papers: Sparse Interactions Reshape Stability in Random Lo…
Nonreciprocal interactions, in which action-reaction symmetry is broken, provide a powerful route to collective dynamics that cannot be captured by equilibrium free-energy minimisation. Here, we introduce and analyse a two-species…
The consensus that complexity begets stability in ecosystems was challenged in the seventies, a result recently extended to ecologically-inspired networks. The approaches assume the existence of a feasible equilibrium, i.e. with positive…
We carry out mathematical analyses, {\em \`{a} la} Helmholtz's and Boltzmann's 1884 studies of monocyclic Newtonian dynamics, for the Lotka-Volterra (LV) equation exhibiting predator-prey oscillations. In doing so a novel "thermodynamic…
We use the Fokker-Planck equation and its moment equations to study the collective behavior of interacting particles in unsteady one-dimensional flows. Particles interact according to a long-range attractive and a short-range repulsive…
Species-rich communities, such as the microbiota or microbial ecosystems, provide key functions for human health and climatic resilience. Increasing effort is being dedicated to design experimental protocols for selecting community-level…
This thesis investigates critical phenomena and equilibrium states in various stochastic models through three interconnected studies. In the first chapter, we analyze the Activated Random Walk model on a one-dimensional ring in the…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
Models of many-species ecosystems, such as the Lotka-Volterra and replicator equations, suggest that these systems generically exhibit near-extinction processes, where population sizes go very close to zero for some time before rebounding,…
The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied. To describe the spatial distributions of the species we use a model based on…
The two-species population dynamics model is the simplest paradigm of interspecies interaction. Here, we include intraspecific competition to the Lotka-Volterra model and solve it analytically. Despite being simple and thoroughly studied,…
We investigate the mean-field dynamics of stochastic McKean differential equations with heterogeneous particle interactions described by large network structures. To express a wide range of graphs, from dense to sparse structures, we…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…
Quantification of chaos is a challenging issue in complex dynamical systems. In this paper, we discuss the chaotic properties of generalized Lotka-Volterra and May-Leonard models of biodiversity, via the Hamming distance density. We…
Both natural ecosystems and biochemical reaction networks involve populations of heterogeneous agents whose cooperative and competitive interactions lead to a rich dynamics of species' abundances, albeit at vastly different scales. The…
Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…
The study of interactions between multiple species in an ecosystem is an active and impactful direction of inquiry. This is true in particular for fragile systems in which even small perturbations of their functional parameters can produce…
This paper is devoted to the stability analysis of an n species Lotka-Volterra system with discrete and distributed delays. Stochastic perturbations to the parameters of the model are allowed. Sufficient conditions for the almost sure…
Niche and neutral theory are two prevailing, yet much debated, ideas in ecology proposed to explain the patterns of biodiversity. Whereas niche theory emphasizes selective differences between species and interspecific interactions in…
Multi-stability is a widely observed phenomenon in real complex networked systems, such as technological infrastructures, ecological systems, gene regulation, transportation and more. When a system functions normally but there exists also a…
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…