Related papers: Analyzing population dynamics models via Sumudu tr…
A technique which is known as Sumudu Transform Method (STM) is studied for the construction of solutions of a most general form of delay differential equations of pantograph type. This is a pioneer study on using the STM to construct the…
Mathematical models of interacting populations are often constructed as systems of differential equations, which describe how populations change with time. Below we study one such model connected to the nonlinear dynamics of a system of…
Since steep declines in a population's size also typically alter its composition, population bottlenecks are considered highly important for evolution. However, despite such significance, the mechanisms governing the impact of a given…
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…
We give a direct proof of well-posedness of solutions to general selection-mutation and structured population models with measures as initial data. This is motivated by the fact that some stationary states of these models are measures and…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
The dynamic theory of inhomogeneous populations developed during the last decade predicts several essential new dynamic regimes applicable even to the well-known, simple population models. We show that, in an inhomogeneous population with a…
We build upon the recent steady-state Penna model solution, Phys.Rev.Lett. 89, 288103 (2002), to study the population dynamics within the Penna model. We show, that any perturbation to the population can be broken into a collection of modes…
Scaling has been proposed as a powerful tool to analyze the properties of complex systems, and in particular for cities where it describes how various properties change with population. The empirical study of scaling on a wide range of…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
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…
Population-based learning paradigms, including evolutionary strategies, Population-Based Training (PBT), and recent model-merging methods, combine fast within-model optimisation with slower population-level adaptation. Despite their…
We develop a continuous mathematical model of population dynamics that describes the sequential emergence of new genotypes under limited resources. The framework models genotype density as a nonlinear flow in mutation space, combining…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
This chapter focuses on variable maturation delay or, more precisely, on the mathematical description of a size-structured population consuming an unstructured resource. When the resource concentration is a known function of time, we can…
We analyze mathematical models of the global human population growth and compare them to actual dynamics of the world population and of the world surplus product. We consider a possibility that the so-called world's demographic transition…
Recent methods have been developed to map single-cell lineage statistics to population growth. Because population growth selects for exponentially rare phenotypes, these methods inherently depend on sampling large deviations from finite…
The population protocol model describes collections of distributed agents that interact in pairs to solve a common task. We consider a dynamic variant of this prominent model, where we assume that an adversary may change the population size…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…