Mode locking and quasiperiodicity in a discrete-time Chialvo neuron model

The two-dimensional parameter spaces of a discrete-time Chialvo neuron model are investigated. Our studies demonstrate that for all our choice of two parameters (i) the fixed point is destabilized via Neimark-Sacker bifurcation; (ii) there exist mode locking structures like Arnold tongues and shrimps, with periods organized in a Farey tree sequence, embedded in quasiperiodic/chaotic region. We determine analytically the location of the parameter sets where Neimark-Sacker bifurcation occurs, and the location on this curve where Arnold tongues of arbitrary period are born. Properties of the transition that follows the so-called two-torus from quasiperiodicity to chaos are presented clearly and proved strictly by using numerical simulations such as bifurcation diagrams, the largest Lyapunov exponent diagram on MATLAB and C++.