1:2 and 1:4 resonances in a two-dimensional discrete Hindmarsh-Rose model

摘要

in this paper, the two-parameter bifurcations of a two-dimensional discrete Hindmarsh-Rose model is discussed. It is shown that the system undergoes 1:2 and 1:4 resonances by using a series of affine transformations and bifurcation theory. The numerical simulations including phase portraits, two-parameter bifurcation diagrams, and maximum Lyapunov exponents diagrams for two different varying parameters in a three-dimensional space, not only illustrate the theoretical analysis, but also display the interesting and complex dynamical behaviors.