Related papers: Solution of the Master Equation for Bak-Sneppen Mo…
The aim of this paper is to emphasize various concepts of dichotomies for evolution equations in Banach spaces, due to the important role they play in the approach of stable, instable and central manifolds. The asymptotic properties of the…
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time…
The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data…
This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the…
The present study gives a mathematical framework for self-evolution within autonomous problem solving systems. Special attention is set on universal abstraction, thereof generation by net block homomorphism, consequently multiple order…
We study the dynamics of the Bak-Sneppen model on small-world networks. For each site in the network, we define a ``connectance,'' which measures the distance to all other sites. We find radically different patterns of activity for…
The generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented. The exact solutions of NDE systems describing the evolution of two interacting populations in two…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…
We study the long-time behavior of solutions of the $k$-Hessian evolution equation $u_t=S_{k}(D^2 u)$, posed on a bounded domain of the $n$-dimensional space with homogeneous boundary conditions. To this end, we construct a separable…
Multispecies reaction-diffusion systems, for which the time evolution equation of correlation functions become a closed set, are considered. A formal solution for the average densities is found. Some special interactions and the exact time…
The two-species population dynamics model is the simplest paradigm of interspecies interaction. Here, we include intraspecific competition to the Lotka-Volterra model and solve it analytically. Despite being simple and thoroughly studied,…
We introduce a new interacting particle system intended to model an example of ecological succession involving two species: the bracken and the european beech. The objective is to exhibit phase transitions by proving that there exist three…
This survey is devoted to the asymptotic behavior of solutions of evolution equations generated by maximal monotone operators in Hilbert spaces. The emphasis is in the comparison of the continuous time trajectories to sequences generated by…
The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance, and sociodynamics. We consider the master equation with periodic transition rates. This may represent an…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
In this paper I describe a cellular automaton model of a multi-species ecosystem, suitable for the study of emergent properties of macroevolution. Unlike majority of ecological models, the number of coexisting species is not fixed. Starting…
We consider an integro-differential model for evolutionary game theory which describes the evolution of a population adopting mixed strategies. Using a reformulation based on the first moments of the solution, we prove some analytical…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
We identify the genetic signature of a selective sweep in a population described by a birth-and-death process with density dependent competition. We study the limit behaviour for large K, where K scales the population size. We focus on two…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…