We conduct computer-assisted analysis of the two-dimensional model of a
neuron introduced by Chialvo in 1995 (Chaos, Solitons & Fractals 5, 461-479).
We apply the method for rigorous analysis of global dynamics based on a
set-oriented topological approach, introduced by Arai et al. in 2009 (SIAM J.
Appl. Dyn. Syst. 8, 757-789) and improved and expanded afterwards.
Additionally, we introduce a new algorithm to analyze the return times inside a
chain recurrent set. Based on this analysis, together with the information on
the size of the chain recurrent set, we develop a new method that allows one to
determine subsets of parameters for which chaotic dynamics may appear. This
approach can be applied to a variety of dynamical systems, and we discuss some
of its practical aspects. The data and the software described in the paper are
available at http://www.pawelpilarczyk.com/neuron/