A Novel Chaotic System With Boomerang-Shaped Equilibrium, Its Circuit Implementation and Application to Sound Encryption

  • Saleh Mobayen
  • Sundarapandian VaidyanathanEmail author
  • Aceng Sambas
  • Sezgin Kaçar
  • Ünal Çavuşoğlu
Research Paper


In the chaos literature, there has been much attention paid to chaotic systems with uncountable equilibrium points such as systems with line equilibrium, curve equilibrium. This paper reports a 3-D chaotic system with a closed curve of equilibrium points, which has the shape of a boomerang. Dynamics of the chaotic system with the boomerang equilibrium has been studied by using phase portraits, bifurcation diagram, Lyapunov exponents and Lyapunov dimension. Also, we design an electronic circuit implementation of the theoretical system to check its feasibility. As an application of the new chaotic system, we have derived new results for sound encryption with the new chaotic system.


Chaos Chaotic systems Curve equilibrium Lyapunov exponents Circuit design Sound encryption 


Compliance with Ethical Standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Electrical Engineering, Faculty of EngineeringUniversity of ZanjanZanjanIran
  2. 2.Research and Development CentreVel Tech UniversityChennai, AvadiIndia
  3. 3.Department of Mechanical EngineeringUniversitas Muhammadiyah TasikmalayaTasikmalayaIndonesia
  4. 4.Department of Electrical and Electronics EngineeringSakarya UniversitySakaryaTurkey
  5. 5.Department of Computer EngineeringSakarya UniversitySakaryaTurkey

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