Related papers: Sustainability Risks under Lotka-Volterra Dynamics
The correctness of Harrods model in the differential form is studied. The inadequacy of exponential growth of economy is shown; an alternative result is obtained. By example of Phillips model, an approach to correction of macroeconomic…
Ecological forecasts are model-based statements about currently unknown ecosystem states in time or space. For a model forecast to be useful to inform decision makers, model validation and verification determine adequateness. The measure of…
Explaining the emergence of self-organized biodiversity and species abundance distribution patterns remians a fundamental challenge in ecology. While classical frameworks, such as neutral theory and models based on pairwise species…
Stochastic Volterra equations (SVEs) serve as mathematical models for the time evolutions of random systems with memory effects and irregular behaviour. We introduce neural stochastic Volterra equations as a physics-inspired architecture,…
Species-rich ecosystems often exhibit multiple stable states with distinct species compositions. Yet, the factors determining the likelihood of each state's occurrence remain poorly understood. Here, we characterize and explain the…
We study a normalized two dimensional competitive Lotka$-$Volterra system describing the interaction between state power and society power. Restricting attention to the positively invariant domain $[0,1]^2$, the analysis focuses on interior…
Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced.…
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Based on the law of mass action (and its microscopic foundation) and mass conservation, we present here a method to derive consistent dynamic models for the time evolution of systems with an arbitrary number of species. Equations are…
Complex Earth System Models are widely utilised to make conditional statements about the future climate under some assumptions about changes in future atmospheric greenhouse gas concentrations; these statements are often referred to as…
We analyse four consecutive cycles observed in the USA for employment and inflation. They are driven by three oil price shocks and an intended interest rate shock. Non-linear coupling between the rate equations for consumer products as prey…
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field…
The scientific data about the state of our planet, presented at the 2012 (Rio+20) summit, documented that today's human family lives even less sustainably than it did in 1992. The data indicate furthermore that the environmental impacts…
Global return values of marine wind speed and significant wave height are estimated from very large aggregates of archived ensemble forecasts at +240-h lead time. Long lead time ensures that the forecasts represent independent draws from…
At the heart of technology transitions lie complex processes of social and industrial dynamics. The quantitative study of sustainability transitions requires modelling work, which necessitates a theory of technology substitution. Many, if…
The deformation-related energy budget is usually considered in the simplest form or even completely omitted from the energy balance equation. We derive a full energy balance equation that accounts not only for heat energy but also for…
This paper introduces the class of volatility modulated L\'{e}vy-driven Volterra (VMLV) processes and their important subclass of L\'{e}vy semistationary (LSS) processes as a new framework for modelling energy spot prices. The main…
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…
Internal climate variability arises from the climate system's inherently chaotic dynamics. Quantifying it is essential for climate science, as it enables risk-based decision-making and differentiates between externally forced change and…
Species coexistence is a complex, multifaceted problem. At an equilibrium, coexistence requires two conditions: stability under small perturbations; and feasibility, meaning all species abundances are positive. Which of these two conditions…