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  3. Simde App: Simulating And Visualizing Formal Theories Using Differential Equations.
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  3. Simde App: Simulating And Visualizing Formal Theories Using Differential Equations.

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SimDE App: Simulating and visualizing formal theories using differential equations.

Rohit Batra1, Emorie D Beck1, Meng Chen2

  • 1Department of Psychology, University of California, Davis.

Psychological Methods
|December 4, 2025

View abstract on PubMed

Summary
This summary is machine-generated.

Formalizing psychological theories with mathematical language, specifically differential equations (DEs), enhances clarity. SimDE, an R Shiny app, translates verbal theories into DE models for simulation and analysis before data collection.

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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.