SimDE App: Simulating and visualizing formal theories using differential equations

Area of Science:

• Psychology
• Computational Neuroscience
• Mathematical Psychology

Background:

• Psychological theories often use verbal language, leading to ambiguous interpretations.
• Formalizing theories mathematically, particularly with differential equations (DEs), offers quantitative precision.
• Existing tools for translating verbal psychological theories into DE models are limited.

Purpose of the Study:

• Introduce SimDE, an R Shiny application designed to bridge the gap between verbal psychological theories and mathematical models.
• Provide researchers with a tool to specify, simulate, and analyze differential equation models derived from psychological theories.
• Facilitate the exploration and refinement of dynamic psychological theories through quantitative modeling.

Main Methods:

• Developed SimDE, an open-access R Shiny application for specifying and simulating differential equation (DE) models.
• The application supports first- or second-order DEs, with or without dynamic error terms (ordinary or stochastic DEs), and includes coupling dynamics.
• Users can plot simulated trajectories to visualize system dynamics and assess model appropriateness.

Main Results:

• SimDE enables users to translate verbal theories into formal DE models.
• The application allows for the simulation of variable trajectories over time for various DE model types.
• Users can visually inspect model behavior to evaluate its fit to psychological phenomena.

Conclusions:

• SimDE serves as a valuable tool for researchers to explore and refine dynamic psychological theories using differential equations.
• The application aids in understanding implicit assumptions within theoretical models before empirical data collection.
• Facilitates quantitative analysis and interpretation of psychological hypotheses through mathematical formalization.