Related papers: Mathematical Model of Easter Island Society Collap…
Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might…
Addressing both natural and societal challenges requires collective cooperation. Studies on collective-risk social dilemmas have shown that individual decisions are influenced by the perceived risk of collective failure. However, existing…
A non-local toy-model is proposed for the purpose of modelling the ``wave function collapse'' of a two-state quantum system. The collapse is driven by a nonlinear evolution equation with an extreme sensitivity to absolute phase. It is…
We consider a moving boundary mathematical model of biological invasion. The model describes the spatiotemporal evolution of two adjacent populations: each population undergoes linear diffusion and logistic growth, and the boundary between…
Although each year brings rapid advancement in meteorology and forecasting technology, the threat of natural disasters is not totally predictable. Predictability, however, still will not guarantee avoidability, thus adequate time to react…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…
We use the most up to date Milky Way model and solar orbit data in order to test the hypothesis that the Sun's galactic spiral arm crossings cause mass extinction events on Earth. To do this, we created a new model of the Milky Way's spiral…
An explanation for the political processes leading to the sudden collapse of empires and states would be useful for understanding both historical and contemporary political events. We seek a general description of state collapse spanning…
Measures of wealth and production have been found to scale superlinearly with the population of a city. Therefore, it makes economic sense for humans to congregate together in dense settlements. A recent model of population dynamics showed…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
Mathematical models of population extinction have a variety of applications in such areas as ecology, paleontology and conservation biology. Here we propose and investigate two types of sub-exponential models of population extinction.The…
We consider systems of interacting diffusions with local population regulation. Our main result shows that the total mass process of such a system is bounded above by the total mass process of a tree of excursions with appropriate drift and…
A relativistic model of a heat conducting collapsing star, which includes thermal pre-relaxation processes, is presented. Particular attention is paid to the influence of a given parameter defined in terms of thermodynamic variables, on the…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state…
Complex evolving systems such as the biosphere, ecosystems and societies exhibit sudden collapses, for reasons that are only partially understood. Here we study this phenomenon using a mathematical model of a system that evolves under…
We consider a possibility of socioeconomic collapse caused by the spread of epidemic. To this end, we exploit a simple SIS-like (susceptible-infected-susceptible) model with negative feedback between the infected population size and a…
We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than…
The probability of the survival of the population of individuals of both sexes of given mature age, procreation rate and structure stability has been searched in the numerical experiment. The populations with long period of reproduction and…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…