PyDSTool

"PyDSTool is an integrated simulation, modeling and analysis package for dynamical systems, written in Python. 

Features implemented:

• Efficient and state-of-the-art ODE / DAE / discrete map simulation tools (using dynamically-linked and automatically generated C code, if external compiler available) (see wiki page)
• Hybrid model and event-driven simulation support (see wiki page)
• Simulations and analysis can be forced to be "bounds safe", e.g. for "non-negativity preservation" (see wiki page)
• Bifurcation analysis and continuation tools in-built, via PyCont
• Support for data-driven modeling (see wiki page)
• Interactive command-line / script-based interface
• "Index-free" and context-heavy data structures, including an enhanced version of arrays (see wiki page)
• Symbolic expression utilities (including evaluation, substitution, derivatives, some simplification) (see wiki page)
• Easy to build complex models using hierarchical object-oriented data structures that contain composable model specifications (see wiki page)
• Memory management utilities, data import & export (inc. basic SBML conversion and LaTeX markup via the SloppyCell package)
• Modular code design allows easy expansion to support other algorithms (contributions welcome)
• Data structures and toolkits for parameter estimation / model fitting and other time-series and data-driven problems
• Seamless use with tools in SciPy, etc. through dynamic typing
• Additional toolboxes for specific applications, including biomechanical modeling, computational neuroscience, and systems biology (see wiki page)
• Many tutorial examples and documentation available online at the wiki

Users of PyDSTool need to be familiar with working in interactive, command-line environments such as UNIX and Matlab, including the writing of simple command scripts. There is presently no graphical interface for PyDSTool. Our emphasis is on the interactivity of a command-line and the rapid prototyping possibilities of script-based computing."

https://wiki.python.org/moin/PyDSTool