Proceeding of International Conference
Amoh Seiya, Ogura Miho, Tetsushi Ueta, A Method to Obtain Variational Equations Automatically by Applying Symbolic Differentiation, Institute of Electronics, Information and Communication Engineers, Proc. NSLW2021, Online, Dec. 2021.
Abstract: In the conventional implementations for solving bifurcation problems, Jacobian matrix and its partial derivatives regarding the given problem should be provided manually. This process is not so easy, thus it often induces human errors like computation failures, mistakes of copies, especially if the system is higher order. In this paper, we develop a preprocessor that gives the Jacobian matrix and partial derivatives symbolically by using SymPy packages on the Python platform. Possibilities about the inclusion of errors are minimized by symbolic derivations and reducing loop structures. It imposes a user only on putting an expression of the equation into a JSON fomat file. We demonstrate bifurcation calculations for discrete neuron dynamical systems. The system includes an exponential function, which makes the calculation of derivatives complicated, but we show that it can be implemented simply by using the symbolic differentiation.