Abstract
In this paper, firstly, asymptotically embedding the fourth iterate of the normal form of a discrete reduced Lorenz system into a flow, we present rigorously the bifurcation sequence as the parameter varies around the 1:4 strong resonance point, from which an Arnold tongue corresponding to a rotation number 1/4 is obtained. Then, by the theory of normal form, we give theoretically the Arnold tongues in the weak resonances such that the system possesses two periodic orbits on the stable invariant closed curve generated from the Neimark–Sacker bifurcation. Furthermore, we obtain rigorously the parameter conditions under which the system has the chaotic behaviour in Marotto's sense. Finally, by numerical simulations, not only our results are verified, but also some new and interesting dynamical behaviours are discovered.
Published Version
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