Related papers: Modes of Growth in Dynamic Systems
The logistic equation is ubiquitous in applied mathematics as a minimal model of saturating growth. Here, we examine a broad generalisation of the logistic growth model to discretely structured populations, motivated by examples that range…
Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human's ecosystem engineering that has profoundly modified the world's landscape. Despite the age-old concern that unchecked population and economic…
Drawing on the understanding of the logistic map, we propose a simple predator-prey model where predators and prey adapt to each other, leading to the co-evolution of the system. The special dynamics observed in periodic windows contribute…
We formulate a model that describes the escape dynamics in a leaky chaotic system in which the size of the leak depends on the number of the in-falling particles. The basic motivation of this work is the astrophysical process which…
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(\sigma(\omega t))x(t)$ where…
Biological systems are modular, and this modularity evolves over time and in different environments. A number of observations have been made of increased modularity in biological systems under increased environmental pressure. We here…
Recently, we developed a theory of a geometrically growing system. Here we show that the theory can explain some phenomena of power-law distribution including classical demographic and economic and novel pandemic instances, without…
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic…
It is still common wisdom amongst economists, politicians and lay people that economic growth is a necessity of our social systems, at least to avoid distributional conflicts. This paper challenges such belief moving from a purely physical…
We prove results on existence and uniqueness of solutions of a system of equations modeling the evolution of a generalized bioconvective flow. The mathematical model considered in the present work describes the convective motion generated…
The theory of natural selection has two forms. Deductive theory describes how populations change over time. One starts with an initial population and some rules for change. From those assumptions, one calculates the future state of the…
The capacity to adapt can greatly influence the success of systems that need to compensate for damaged parts, learn how to achieve robust performance in new environments, or exploit novel opportunities that originate from new technological…
Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination…
We study the multi-scale description of large-time collective behavior of agents driven by alignment. The resulting multi-flock dynamics arises naturally with realistic initial configurations consisting of multiple spatial scaling, which in…
We investigate the selective forces that promote the emergence of modularity in nature. We demonstrate the spontaneous emergence of modularity in a population of individuals that evolve in a changing environment. We show that the level of…
We have generalized our ``unified'' model of evolutionary ecology by taking into account the possible movements of the organisms from one ``patch'' to another within the same eco-system. We model the spatial extension of the eco-system…
Plants solve complex problems without centralized control, relying instead on growth-driven dynamics to sense, navigate, and optimize resource acquisition. This review presents a unified physical framework for understanding plant behavior…
Population-level scaling in ecological systems arises from individual growth and death with competitive constraints. We build on a minimal dynamical model of metabolic growth where the tension between individual growth and mortality…
This paper introduces a variational formulation of natural selection, paying special attention to the nature of "things" and the way that different "kinds" of "things" are individuated from - and influence - each other. We use the Bayesian…
We consider a parameter dependent periodic-logistic problem with a logistic term involving a degeneracy that replicates time dependent refuges in the habitat of a population. Working under no or very minimal assumptions on the boundary…