Existence and Control of Hidden Oscillations in a Memristive Autonomous Duffing Oscillator

  • Vaibhav Varshney
  • S. Sabarathinam
  • K. Thamilmaran
  • M. D. Shrimali
  • Awadhesh Prasad
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 133)


Studying the memristor based chaotic circuit and their dynamical analysis has been an increasing interest in recent years because of its nonvolatile memory. It is very important in dynamic memory elements and neural synapses. In this chapter, the recent and emerging phenomenon such as hidden oscillation is studied by the new implemented memristor based autonomous Duffing oscillator. The stability of the proposed system is studied thoroughly using basin plots and eigenvalues. We have observed a different type of hidden attractors in a wide range of the system parameters. We have shown that hidden oscillations can exist not only in piecewise linear but also in smooth nonlinear circuits and systems. In addition, to control the hidden oscillation, the linear augmentation technique is used by stabilizing a steady state of augmented system.


Memristor system Hidden oscillations Linear augmentation Memristor stability 



Vaibhav Varshney, Awadhesh Prasad and acknowledge DST, Government of India for the financial support. S. Sabarathinam acknowledges the DST-SERB for the financial assistance through National Post Doctoral Fellow (NPDF) scheme. K. Thamilmaran acknowledge DST PURSE scheme for financial assisitance and Awadhesh Prasad and M. D. Shrimali also acknowledge joint project DST-RFBR for funding.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Vaibhav Varshney
    • 1
  • S. Sabarathinam
    • 1
  • K. Thamilmaran
    • 3
  • M. D. Shrimali
    • 2
  • Awadhesh Prasad
    • 1
  1. 1.Department of Physics and AstrophysicsUniversity of DelhiDelhiIndia
  2. 2.Department of PhysicsCentral University of RajasthanAjmerIndia
  3. 3.School of PhysicsCentre for Nonlinear Dynamics, Bharathidasan UniversityTiruchirappalliIndia

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