By the authors’ reckoning, modeling needs an established body of knowledge, usable by all specialists in the discipline.
This work begins by explaining concepts related to the levels of system specification and their formalism (both computationally and mathematically). In particular, it mentions the need for hierarchical decomposition and system descriptions from the view of continuity or separated events, that is, differential equations, difference equations, and discrete events.
For each event, whatever the formalism that models it, when it undergoes a state transition, it may need to be coupled with the components of an entire system. The authors use the language of morphisms, particularly homomorphisms, to refer to the relations between single-state transitions and multiple-state transitions. In mathematics, a homomorphism is a function that preserves operations defined within objects. Indeed, microstate transitions get preserved within macrostates, thus respecting granularity once it is defined.
The work then discusses discrete-time models such as Conway’s Game of Life as successful computational strategies for self-sustaining, independent entities that interact.
For the hands-on work connected with this book, readers can use a simulation environment; the book describes DEVSJAVA.
The book also discusses numerical issues with the models, for example, the convergence toward solving ordinary differential equations under different numerical schemes, and even the Lipschitz condition for discrete event system specification (DEVS). The intent is not just to expose errors in the numerical approximations, but also their effects in event representation.
This work uses concepts from homological algebra, such as commutative diagrams, for some general explanations; functional notation, pseudocode, and code itself are used sparingly (as XMILE, an open standard for system dynamics modeling). The book ends with spiking neuron modeling through iterative specification and DEVS Markov models.
I highly recommend this book to mathematicians and computer specialists in simulation, as well as more general professionals and advanced undergraduates who would like to better understand modeling.