Related papers: Effective one-dimension reduction of multi-compart…
A dynamical model of an ecological community is analyzed within a "mean-field approximation" in which one of the species interacts with the combination of all of the other species in the community. Within this approximation the model may be…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and…
Complex dynamical systems are prevalent in various domains, but their analysis and prediction are hindered by their high dimensionality and nonlinearity. Dimensionality reduction techniques can simplify the system dynamics by reducing the…
We discuss the relevance of studying ecology within the framework of Complexity Science from a statistical mechanics approach. Ecology is concerned with understanding how systems level properties emerge out of the multitude of interactions…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
Dynamical networks are powerful tools for modeling a broad range of complex systems, including financial markets, brains, and ecosystems. They encode how the basic elements (nodes) of these systems interact altogether (via links) and evolve…
Complex systems are fascinating because their rich macroscopic properties emerge from the interaction of many simple parts. Understanding the building principles of these emergent phenomena in nature requires assessing natural complex…
The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical…
Dynamics of species' abundances in ecological communities are often described using models that only account for a few species. It is not clear when and why this would be possible, as most species form part of diverse ecological…
In this work, we introduce a quantum-inspired epidemic model to study the dynamics of an infectious disease in a population divided into compartments. By treating the healthy population as a large reservoir, we construct a framework based…
A complex system comprises multiple interacting entities whose interdependencies form a unified whole, exhibiting emergent behaviours not present in individual components. Examples include the human brain, living cells, soft matter, Earth's…
Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the…
Deterministic compartmental models have been used extensively in modeling epidemic propagation. These models are required to fit available data and numerical procedures are often implemented to this end. But not every model architecture is…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…