Articles written in Pramana – Journal of Physics

    • Hidden attractors without equilibrium and adaptive reduced-order function projective synchronization from hyperchaotic Rikitake system


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      By introducing an additional state feedback into classic Rikitake system, a new hyperchaotic system without equilibrium is derived. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincaré maps. Based on adaptive control and Lyapunov stability theory, we design a reduced-order projective synchronization scheme for synchronizing the hyperchaotic Rikitake system coexisting without equilibria and the original classic Rikitake system coexisting with two non-hyperbolic equilibria. Finally, numerical simulations are given to illustrate the effectiveness of the proposedsynchronization scheme.

    • Degenerate Hopf bifurcation in a self-exciting Faraday disc dynamo


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      In order to further understand a self-exciting Faraday disc dynamo (Hide $\it{et al}$, in $\it{Proc. R. Soc}.$ A $\bf{452}$, 1369 1996), showing chaotic attractors with very complicated topological structures, we present codimension one and two (degenerate) Hopf bifurcations and prove the existence of periodic solutions. In addition, numerical simulations are given for confirming the theoretical results.

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