Kalmar-Nagy, TamasStanciulescu, Ilinca2014-07-302014-07-302014Kalmar-Nagy, Tamas and Stanciulescu, Ilinca. "Can complex systems really be simulated?." <i>Applied Mathematics and Computation,</i> 227, (2014) Association for Computing Machinery: 199-211. http://dx.doi.org/10.1016/j.amc.2013.11.037.https://hdl.handle.net/1911/76291The simulation of complex systems is important in many fields of science and in real-world applications. Such systems are composed of many interacting subsystems. There might exist different software packages for simulating the individual subsystems and co-simulation refers to the simultaneous execution of multiple interacting subsystem simulators. Simulation or co-simulation, if not designed properly, can return misleading numerical solutions (unstable numerical solutions for what is in fact a stable system or vice versa). To understand the cause of these numerical artifacts, we first propose a simple mathematical model for co-simulation, and then construct stability charts. These charts shed light on transitions between stable and unstable behaviour in co-simulation. Our goal is to understand the stability properties of the simulated and co-simulated representation of the continuous system. We will achieve this goal by expressing the trace and determinant of the discretized system in terms of the trace and determinant of the continuous system to establish stability criteria.engThis is an author's peer-reviewed final manuscript, as accepted by the publisher. The published article is copyrighted by the Association for Computing Machinery.Journal articlestabilitysimulation and co-simulationstability boundarieshttp://dx.doi.org/10.1016/j.amc.2013.11.037