SimDE App: Simulating and visualizing formal theories using differential equations

Psychological theories are often expressed verbally using natural language, which may lead to varying interpretations of the phenomenon under study. This potential confusion can be mitigated by formalizing verbal theories using mathematical language, which can help in defining, analyzing, and interpreting one's hypotheses in quantitative terms. Differential equations (DEs) are a class of models in the dynamical systems framework, particularly suited to many dynamic theories in psychology. However, there is a lack of tools for translating verbal theories into DE systems. To facilitate this translation, we introduce SimDE (https://simde.ucdavis.edu/), an open-access R Shiny application that allows users to specify a DE model and then simulate the trajectories of each variable over time. SimDE provides an interface to simulate a range of DE models, with features such as: (a) first- or second-order DEs (e.g., exponential, oscillatory), (b) models with or without a dynamic error term (ordinary or stochastic DEs), (c) models with coupling dynamics. Users have the flexibility of plotting these systems in order to see the pattern of changes over time and determine the appropriateness of the model for the phenomenon they are trying to study. The goal of our app is to serve as a tool for researchers who want to explore DE models for their psychological theories before they even collect data. It can also help researchers to study the implicit assumptions of their systems defined with such DEs and further refine them as needed. (PsycInfo Database Record (c) 2026 APA, all rights reserved).