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\begin{document}

\title{Bifurcation and comparison of a discrete-time Hindmarsh-Rose model}



\author[1]{Yue Li}%
\author[1]{Hongjun Cao}%
\affil[1]{Beijing Jiaotong University}%


\vspace{-1em}



  
  \date{May 27, 2024}


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\begin{abstract}
In this paper, a discrete-time Hindmarsh-Rose model is obtained by a
nonstandard finite difference (NSFD) scheme. Bifurcation behaviors
between the model obtained by the forward Euler scheme and the model
obtained by the NSFD scheme are compared. Through analytical and
numerical comparisons, much more bifurcations and dynamical behaviors
can be obtained and preserved by using the NSFD scheme, in which the
integral step size can be chosen larger relatively due to its better
stability and convergence than those in the forward Euler scheme. It
means that the discretetime model obtained by the NSFD scheme is closer
to the original continuous system than the discrete-time model obtained
by the forward Euler scheme. These confirmed results can at least
guarantee true available numerical results to investigate complex neuron
dynamical systems.%
\end{abstract}%



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