Structure-preserving numerical integrators for hodgkin-huxley-type systems

Zhengdao Chen, Baranidharan Raman, Ari Stern

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Motivated by the Hodgkin-Huxley model of neuronal dynamics, we study explicit numerical integrators for "conditionally linear"" systems of ordinary differential equations. We show that splitting and composition methods, when applied to the Van der Pol oscillator and to the Hodgkin-Huxley model, do a better job of preserving limit cycles of these systems for large time steps, compared with the "Euler-type"" methods (including Euler's method, exponential Euler, and semi-implicit Euler) commonly used in computational neuroscience, with no increase in computational cost. These limit cycles are important to preserve, due to their role in neuronal spiking. Splitting methods even compare favorably to the explicit exponential midpoint method, which is twice as expensive per step. The second-order Strang splitting method is seen to perform especially well across a range of nonstiff and stiff dynamics.

Original languageEnglish
Pages (from-to)B273-B298
JournalSIAM Journal on Scientific Computing
Issue number1
StatePublished - 2020


  • Computational neuroscience
  • Exponential integrators
  • Hodgkin-Huxley
  • Limit cycles
  • Splitting methods
  • Van der Pol oscillator


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