A new 4-D hyperchaotic hidden attractor system: its dynamics, coexisting attractors, synchronization and microcontroller implementation

Basil Hani Jasim, Kadhim H. Hassan, Khulood Moosa Omran


In this paper, a simple 4-dimensional hyperchaotic system is introduced. The proposed system has no equilibria points, so it admits hidden attractor which is an interesting feature of chaotic systems. Another interesting feature of the proposed system is the coexisting of attractors where it shows periodic and chaotic coexisting attractors. After introducing the system, the system is analyzed dynamically using numerical and theoretical techniques. In this analysis, Lyapunov exponents and bifurcation diagrams have been used to investigate chaotic and hyperchaotic nature, the ranges of system parameters for different behaviors and the route for chaos and coexisting attractors regions. Theoretical analysis includes finding some of the important properties of the system such as Lyapunov dimension, dissipation and symmetry. In the next part of our work, a synchronization control system for two identical systems is designed. The design procedure uses a combination of simple synergetic control with adaptive updating laws to identify the unknown parameters derived basing on Lyapunov theorem. Microcontroller (MCU) based hardware implementation system is proposed and tested by using Matlab as a display side. As an application, the designed synchronization system is used as a secure analog communication system. The designed MCU system with Matlab Simulation is used to validate the designed synchronization and secure communication systems and excellent results have been obtained where a very small error between the two synchronized systems and the transmitted and received signals have been obtained in a very small time.


chaotic; coexisting attractors; hidden attractor; hyperchaotic synchronization;

DOI: http://doi.org/10.11591/ijece.v11i3.pp%25p
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ISSN 2088-8708, e-ISSN 2722-2578