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Berkeley Madonna

Differential equations solver with graphical interface for constructing and analyzing complex mathematical models.

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Overview

Berkeley Madonna is a general-purpose differential equations solver developed for modeling and analysis of dynamical systems. The software provides a graphical interface that allows users to construct complex mathematical models using symbols rather than writing equations directly, making it accessible to researchers and professionals across a wide range of scientific disciplines.

The platform is used in academic, research, and professional settings, with documented applications spanning cellular biology at UC Berkeley, HIV gene expression research at UCSF and the Gladstone Institute, battery performance modeling for the European Space Agency's Mars Express spacecraft, and conservation biology work at Conservation International.

Version 10 Highlights

  • Runs 2–5 times faster than previous versions, with support for large, memory-intensive models
  • 64-bit architecture enabling handling of larger model sizes
  • Compatible with macOS Catalina and later, including Apple M1 and M2 chips
  • Compatible with current and planned Windows operating systems
  • Free upgrade for all existing version 9 users
  • A published tutorial paper describing new features in version 10, including construction of a classic PBPK model, is available as a free download

Core Capabilities

  • Intuitive graphical interface with toolbar icons for building models; equations are written automatically as the model is constructed
  • One-click execution that solves equations and plots results immediately
  • Automatic graphing of results with interactive sliders for exploring the effect of changing parameter values
  • Additional visualization tools including parameter plot and fast Fourier transform
  • Support for multiple integration schemes to solve ordinary differential equations (ODEs), difference equations, and discrete simulations
  • Curve fitting interface for extracting parameter estimates from data
  • Batch runs functionality for plotting results across a sweep of parameter values

Licensing and Deployment

  • Available in three license tiers: Education, Academic, and Professional
  • Desktop software compatible with both macOS and Windows platforms

Berkeley Madonna is developed at UC Berkeley and serves a broad user base ranging from students and academic researchers to professional scientists in fields including pharmacokinetics, space science, virology, and ecology.