期刊
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
卷 56, 期 -, 页码 481-489出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2017.08.027
关键词
Chialvo neuron model; Parameter space; Arnold tongue; Farey tree; Largest Lyapunov exponents
类别
资金
- Natural Science Foundation of China (NSFC) [11171017]
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++. (C) 2017 Elsevier B.V. All rights reserved.
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