Nonlinear Dynamics

, Volume 93, Issue 3, pp 1087–1108 | Cite as

Modified jerk system with self-exciting and hidden flows and the effect of time delays on existence of multi-stability

  • Karthikeyan Rajagopal
  • Sajad Jafari
  • Akif Akgul
  • Anitha Karthikeyan
Original Paper


In this paper, we report a new chaotic jerk system which shows self-excited and hidden oscillations depending on its parameters. Dynamic analysis shows that the proposed system exhibits multi-stability and coexisting attractors. To study the effect of time delays on the multi-stability feature of the system, we introduce multiple time delays in the third state variable. Investigation of dynamical properties of the time-delayed system shows the disappearance of multi-stability. Such a feature has not been reported earlier in the literatures.


Jerk systems Hidden oscillations Bifurcation Multi-stability Time-delayed systems FPGA implementation 


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Authors and Affiliations

  1. 1.Centre for Non-linear DynamicsDefense UniversityBishoftuEthiopia
  2. 2.Biomedical Engineering DepartmentAmirkabir University of TechnologyTehranIran
  3. 3.Department of Electrical and Electronics Engineering, Faculty of TechnologySakarya UniversitySakaryaTurkey
  4. 4.Department of Electronics EngineeringChennai Institute of TechnologyChennaiIndia

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