Affiliation:
1. Department of Mathematical Sciences and Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
Abstract
<p style='text-indent:20px;'>The present work is devoted to giving new insights into the Hide-Skeldon-Acheson (HSA) dynamo. The paper discusses the locally and globally asymptotical stability of the equilibrium. All orbits of the system are proved to be bounded. The existence of periodic orbits is proved by the generalized Melnikov method. The paper proves rigorously that Hopf bifurcation occurs and gives the formulae to determine the direction, stability and period of bifurcating periodic solutions. Finally, the paper investigates the coexistence of three types of attractors: equilibria, hidden periodic attractors and hidden chaotic attractors.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics
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