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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.

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