Related papers: Modelling the longevity of complex living systems
Recently we have extended our the "unified" model of evolutionary ecology to incorporate the {\it spatial inhomogeneities} of the eco-system and the {\it migration} of individual organisms from one patch to another within the same…
These are notes from elementary lectures given in the summer of 2013 at the YMSC center at Tsinghua University in Beijing.
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Air transport systems are highly dynamic at temporal scales from minutes to years. This dynamic behavior not only characterizes the evolution of the system but also affect the system's functioning. Understanding the evolutionary mechanisms…
We study discrete Laplacians on two-dimensional lattices under modular iterations, focusing on the emergence of nontrivial large-scale patterns. While purely binary or constant modular sequences quickly collapse into strict periodicity, the…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…
We provide a general overview of the velocity-dependent one-scale model for cosmic string evolution and discuss two further extensions to it. We introduce and justify a new ansatz for the momentum parameter $k$, and also incorporate the…
We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction…
This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper [6]. The improvement is explained in Section 1 and proved in Section 2. The importance of the extension is demonstrated in Section 3 with an…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General…
This is the final version of the lecture notes of the 23rd Internet Seminar on Evolutionary Equations, see also https://www.mat.tuhh.de/isem23/.
A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…
We analyze the structure of DNA molecules of different organisms by using the additive Markov chain approach. Transforming nucleotide sequences into binary strings, we perform statistical analysis of the corresponding "texts". We develop…
Ecological systems are governed by complex interactions which are mainly nonlinear. In order to capture this complexity and nonlinearity, statistical models recently gained popularity. However, although these models are commonly applied in…
We combine incentive, adaptive, and time-scale dynamics to study multipopulation dynamics on the simplex equipped with a large class of Riemmanian metrics, simultaneously generalizing and extending many dynamics commonly studied in dynamic…
This paper develops the basic analytical theory related to some recently introduced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of $\reali^+$. The results on the stability with…
Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many…
This paper contains the lectures I delivered during the 37th Saas-Fee Advanced Course in March 2007. It reviews all the main ingredients necessary to build galactic chemical evolution models with particular attention to the Milky Way and…
This survey is an in-depth development of the theoretical aspects of the method of Evolving Sets, a method which has been used in several of my papers. It is fairly esoteric as to a large degree it stems from my efforts to ascertain whether…