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1:2 and 1:4 resonances in a two-dimensional discrete Hindmarsh-Rose model. (English) Zbl 1331.92031
Summary: 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.

MSC:
92C20 Neural biology
34F15 Resonance phenomena for ordinary differential equations involving randomness
65L07 Numerical investigation of stability of solutions
37N25 Dynamical systems in biology
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