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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Springer Netherlands

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DOI

10.1016/0094-730x(83)90008-6

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1573-269X

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Bifurcations and chaos in a twodimensional discre

Authors: Bo Li Zhimin He
Publish Date: 2013/12/03
Volume: 76, Issue: 1, Pages: 697-715
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Abstract

In this paper the dynamics of a twodimensional discrete Hindmarsh–Rose model is discussed It is shown that the system undergoes flip bifurcation Neimark–Sacker bifurcation and 11 resonance by using a center manifold theorem and bifurcation theory Furthermore we present the numerical simulations not only to illustrate our results with the theoretical analysis but also to exhibit the complex dynamical behaviors including orbits of period 3 6 15 cascades of perioddoubling bifurcation in orbits of period 2 4 8 16 quasiperiodic orbits and chaotic sets These results obtained in this paper show far richer dynamics of the discrete Hindmarsh–Rose model compared with the corresponding continuous model

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