Parameter values for topological chaos in the reduced Chialvo model

The following dataset is connected with a map-based neuron model introduced by D. Chialvo (Chaos, Solitons & Fractals, 5 (3-4) 1995). The reduced version of this model is a one dimensional discrete system which describes the evolution of the membrane voltage when the value of the second variable, the recovery variable, is fixed. We have recently derived a theorem establishing a combinatorial condition for the orbit of the critical point of the reduced Chialvo map under which the model displays chaos (in the sense of Li-Yorke, Block-Coppel and Devaney). Further information can be found in the file Description_TopologicalChaosChialvo.pdf. The dataset contains also the Matlab file (r_vs_k_up.m) which in a given discretized range of r and k values (where k is the input current) finds those (r,k) pairs for which the condition is satisfied and thus the model displays chaos. The program produces a figure with these values depicted and the Excel table where the first row has the values of r and the corresponding values of k, that satisfy the condition, are listed below in columns. Exemplary figure (Chaos_Parameters.png) and xlsx file (chaoticvalues.xlsx) are contained as well. We remark that the program can be easily modified for any other unimodal interval map, for which our condition applies.