One Simple Model—Various Complex Systems

  • Urszula ForyśEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)


In this chapter we consider a simple system of two ODEs that could be used to describe various phenomena. Examples of these phenomena are presented. In general, we focus on two interacting agents, like two animal populations, two people or groups of people, two neuronal populations and so on. The system have the following structure: the first part of an equation describes the inner dynamics, while the second part is responsible for interactions. We consider two actors/agents having similar inner dynamics, as well as interaction function is similar for both of them. In the simplest case, when the inner dynamics is linear, the behavior of the system depends on the interaction functions. We discuss similarities and differences between the models with different interaction terms.


Ordinary differential equations Mathematical modeling of interacting agents Stability analysis 


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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Faculty of Mathematics, Informatics and Mechanics, Institute of Applied Mathematics and MechanicsUniversity of WarsawWarsawPoland

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