A modified numerical method for bifurcations of fixed points of ODE systems with periodically pulsed inputs

• A modified numerical method for bifurcations of fixed points is constructed.
• The numerical method is applied to ODE systems with periodically pulsed inputs.
• Parallel computation is used to reduce the computation time.
• This numerical method is shown to be much more efficient than our previous method.
• Two-parameter and three-parameter bifurcation diagrams are computed.

Biological systems are often modeled by ordinary differential equations (ODEs). Bifurcation analysis of these mathematical models is important for the study of biological properties. An adaptive grid method in our previous work has been successfully applied to continuous dynamical systems for bifurcations of equilibria. In this paper, the numerical method is modified for the bifurcations of fixed points of ODE systems with periodically pulsed inputs. Two-parameter and three-parameter bifurcation diagrams are computed using a fairly general predator–prey system and the FitzHugh–Nagumo model with pulsed inputs. The parallel computation of the numerical method is also discussed.