Nonlinear Dynamics

, Volume 91, Issue 2, pp 957–974 | Cite as

A chaotic memcapacitor oscillator with two unstable equilibriums and its fractional form with engineering applications

  • Karthikeyan Rajagopal
  • Akif AkgulEmail author
  • Sajad Jafari
  • Burak Aricioglu
Original Paper


A novel charge-controlled memcapacitor 3D chaotic oscillator with two unstable equilibriums is proposed. Various dynamic properties of the proposed system are derived and investigated to show the existence of chaotic oscillations. Fractional-order analysis of the chaotic oscillator shows that the maximum value for the largest positive Lyapunov exponent is exhibited in fractional order. Adomian decomposition method is used to discretize the fractional-order system. Field-programmable gate arrays are used to realize the proposed oscillator. In addition, random number generator is designed by employing this novel chaotic system in its fractional-order form.


Memcapacitor Bifurcation Bicoherence Fractional order Circuit implementation FPGA RNG design 



This work was partially supported by Sakarya University Scientific Research Projects Unit under Grants 2016-09-00-008, 2016-50-01-026. It was also partially supported by Iran National Science Foundation (No. 96000815). The authors thank Mr. Soroush Dehghan and Mr. Navid Hasanzadeh for help and comments which enhanced the quality of this paper.


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Authors and Affiliations

  1. 1.Department of Electrical and Communication EngineeringThe PNG University of TechnologyLaePapua New Guinea
  2. 2.Department of Electrical and Electronics Engineering, Faculty of TechnologySakarya UniversitySakaryaTurkey
  3. 3.Biomedical Engineering DepartmentAmirkabir University of TechnologyTehranIran

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