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

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      https://www.ias.ac.in/article/fulltext/pram/088/04/0062

    • Keywords

       

      Hyperchaos; hidden attractors; reduced order; projective synchronization; Lyapunov stability theorem

    • Abstract

       

      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.

    • Author Affiliations

       

      YU FENG1 WEIQUAN PAN2

      1. Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, People’s Republic of China
      2. School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, People’s Republic of China
    • Dates

       
  • Pramana – Journal of Physics | News

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