Emerging Spatiotemporal Patterns from Discrete Migration Dynamics of Heterogeneous Agents

We propose a discrete agent-based model to investigate the migration dynamics of heterogeneous individuals. Compatibility among agents of different types is expressed in terms of homophily parameters capturing the extent to which similar individuals are attracted to, or dissimilar individuals are repelled by, each other. Based on agent-based simulations, we establish the connection between emerging spatiotemporal patterns and the homophily parameters. Key results are presented in a novel phase diagram, which reveals a wide range of spatial patterns including the cell, worm, herd, amoeba, and swarm modes under the dynamic regime and the separation, ghetto, and integration modes under the stationary one. Our model thus provides a generalized framework encompassing both static equilibrium and nonstationary systems to investigate the impact of agent heterogeneity on population dynamics. We demonstrate potential applications of our model to social systems using sexual segregation of ungulate habitats as a case study

Model Replication in the Context of Agent-Based Simulation: Lessons Learnt from Two Case Studies

This paper examines model replication in the context of agent-based simulation through two case studies. Replication of a computational model and validation of its results is an essential tool for scientific researchers, but it is rarely used by modelers. In our work we address the question of validating and verifying simulations in general, and summarize our experience in approaching different models through replication with different motivations. Two models are discussed in details. The first one is an agent-based spatial adaptation of a numerical model, while the second experiment addresses the exact replication of an existing economic model

Validating an agent-based model of the Zipf׳s Law: A discrete Markov-chain approach

AbstractThis study discusses the validation of an agent-based model of emergent city systems with heterogeneous agents. To this end, it proposes a simplified version of the original agent-based model and subjects it to mathematical analysis. The proposed model is transformed into an analytically tractable discrete Markov model, and its city size distribution is examined. Its discrete nature allows the Markov model to be used to validate the algorithms of computational agent-based models. We show that the Markov chains lead to a power-law distribution when the ranges of migration options are randomly distributed across the agent population. We also identify sufficient conditions under which the Markov chains produce the Zipf׳s Law, which has never been done within a discrete framework. The conditions under which our simplified model yields the Zipf׳s Law are in agreement with, and thus validate, the configurations of the original heterogeneous agent-based model

Markov chain analysis of an agent based growth model

In this paper we investigate the asymptotic behavior of a discrete and probabilistic dynamical system which can be described as a growth model where autonomous agents aggregates. The aim of this paper is to give a mathematical analysis of the dynamics. The analysis uses face homogeneous Markov chains and thanks to this study we validate a conjecture set by Laszlo Gulyas and Yuri Mansury concerning a growth model for cities where simulations had shown that the sizes of the cities asymptotically distribute as a Zipf's law. In light of our analysis, we discuss how the emergence of such a Zipf's law could be expected in Gulyas-Mansury' model and in its variants

A Growth Model for Multicellular Tumor Spheroids

Most organisms grow according to simple laws, which in principle can be derived from energy conservation and scaling arguments, critically dependent on the relation between the metabolic rate B of energy flow and the organism mass m. Although this relation is generally recognized to be of the form B(m) = mp, the specific value of the exponent p is the object of an ongoing debate, with many mechanisms being postulated to support different predictions. We propose that multicellular tumor spheroids provide an ideal experimental model system for testing these allometric growth theories, especially under controlled conditions of malnourishment and applied mechanical stress