TY - JOUR
T1 - Ultradiscrete bifurcations for one dimensional dynamical systems
AU - Ohmori, Shousuke
AU - Yamazaki, Yoshihiro
N1 - Funding Information:
The authors are grateful to Professor D. Takahashi, Professor T. Yamamoto, and Professor Emeritus A. Kitada at Waseda University for useful suggestions and encouragement. We also greatly appreciate the valuable comments from a reviewer. This work was supported by Sumitomo Foundation, Grant No. 200146.
Publisher Copyright:
© 2020 Author(s).
PY - 2020/12/1
Y1 - 2020/12/1
N2 - Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscrete equations. The ultradiscrete equations are derived from normal forms of one-dimensional nonlinear differential equations, each of which has saddle-node, transcritical, or supercritical pitchfork bifurcations. An additional bifurcation, which is similar to the flip bifurcation, is found in ultradiscrete equations for supercritical pitchfork bifurcations. Dynamical properties of these ultradiscrete bifurcations can be characterized with graphical analysis. As an example of application of our treatment, we focus on an ultradiscrete equation of the FitzHugh-Nagumo model and discuss its dynamical properties.
AB - Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscrete equations. The ultradiscrete equations are derived from normal forms of one-dimensional nonlinear differential equations, each of which has saddle-node, transcritical, or supercritical pitchfork bifurcations. An additional bifurcation, which is similar to the flip bifurcation, is found in ultradiscrete equations for supercritical pitchfork bifurcations. Dynamical properties of these ultradiscrete bifurcations can be characterized with graphical analysis. As an example of application of our treatment, we focus on an ultradiscrete equation of the FitzHugh-Nagumo model and discuss its dynamical properties.
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U2 - 10.1063/5.0012772
DO - 10.1063/5.0012772
M3 - Article
AN - SCOPUS:85099649395
SN - 0022-2488
VL - 61
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 12
M1 - 122702
ER -