Center for Nonlinear Systems (CNS)

About the Center:

The Center for Nonlinear Systems (CNS) is an extension research division of Center for Nonlinear Dynamics, Institute of Research and Development, Ministry of National Defense, Ethiopia. CNS is a core research facility focused towards various research activities in the areas related to Nonlinear Systems, Dynamics and Control.


Create a world class research facility to Identify and study complex nonlinear phenomena different approaches and methodologies and apply them to investigate nonlinear physical systems.


  • Identify and study complex nonlinear phenomena using a diverse set of research approaches and methodologies, particularly those of Nonlinear Dynamics, nonlinear science, Secure Communication and Cryptography.

  • Promote the use of scientific results in applied research.

  • Stimulate the formation of interdisciplinary approaches to complex problems.

  • Facilitate the interchange of scientific results and ideas between Laboratory scientists and external centers of excellence.

  • Encourage the exploration of new scientific frontiers at the interface between conventional disciplines.

  • Support a broad spectrum of interdisciplinary science that underpins the Laboratory’s mission in national security.

Specific Objectives:

  • Create International pool of expert team for various joint researches in Non-Linear Dynamics.

  • Create a university environment of innovation: CNS will bring together research and education across a broad spectrum of Nonlinear Dynamics in order to foster multidisciplinary discoveries and inventions that arise through the mixing of students, faculty and researchers across traditional disciplinary boundaries.

  • Integrate education and research: in addition to course work, graduate students will participate in research throughout their education; each CNS faculty member will both teach and engage in research.

  • Develop and embed university components of an innovation and entrepreneurship ecosystem within India. These university components include formal and informal education in Nonlinear Dynamics, as well as university policies and structures for interfacing with industrial commercialization and venture opportunities as they develop at University and elsewhere.

  • Lay the foundation for a world-class research center that will help attract, create, and retain both Indian and international talent to CIT.

  • Create External funding opportunities.

Thrust Areas

Call for various Research positions

List of Publication


1. Alireza Bahramian, Fatemeh Parastesh, Viet-Thanh Pham, Tomasz Kapitaniak, Sajad Jafari, and Matjaž Perc, “Collective behavior in a two-layer neuronal network with time-varying chemical connections that are controlled by a Petri net”, Chaos 31, 033138 (2021); https://doi.org/10.1063/5.0045840. Impact factor – 2.832.

2. M. Mehrabbeik, R. Ramamoorthy, Karthikeyan Rajagopal, F. Nazarimehr, S. Jafari, I. Hussain, Investigating Critical Slowing Down Indicators in Synchronous Period-Doubling for Flicker Vision of Salamander and Man, European Physical Journal – Special Topics, Accepted and Inpress. Impact factor – 1.660.

3. Balamurali Ramakrishnan, Irene Moroz, Chunbiao Li, Anitha Karthikeyan, Karthikeyan Rajagopal, Effects of Noise on the wave propagation in an excitable media with magnetic induction, European Physical Journal – Special Topics, Accepted and Inpress. Impact factor – 1.660.

4. Amor Menaceur, Salah Mahmoud Boulaaras, Amar Makhlouf, Karthikeyan Rajagopal, and Mohamed Abdalla, “Limit Cycles of a Class of Perturbed Differential Systems via the First-Order Averaging Method”, Complexity, Volume 2021, Article ID 5581423, https://doi.org/10.1155/2021/5581423, 2021, Impact factor – 2.680.

5. Sajad Jafari, Karthikeyan Rajagopal, Yasser Shekofteh, Fahimeh Nazarimehr, Chunbiao Li, “A new chaotic multi-stable hyperjerk system with various types of attractors”, Indian Journal of Physics, Accepted and Inpress, 2021, Impact factor – 1.407.

6. Karthikeyan Rajagopal, Sajad Jafari, Chunbiao Li, Anitha Karthikeyan  Prakash Duraisamy, “Suppressing spiral waves in a lattice array of coupled neurons using delayed asymmetric synapse coupling”, Chaos, Solitons and Fractals, Volume 146, 110855, 2021, Impact factor – 3.764.

7. Junxia Wang, Li Xiao, Karthikeyan Rajagopal, Akif Akgul, Serdar Cicek and Burak Aricioglu, “Fractional-Order Analysis of Modified Chua’s Circuit System with the Smooth Degree of 3 and Its Microcontroller-Based Implementation with Analog Circuit Design”, Symmetry , 13(2),340; https://doi.org/10.3390/sym13020340, 2021, Impact factor – 2.645.

8. Anitha Karthikeyan, Karthikeyan Rajagopal, Victor Kamdoum Tamba, Girma Adam,  Ashok kumar Srinivasan, “A simple chaotic Wien bridge oscillator with fractional order memristor and its combination synchronization for efficient anti – attack capability”, Complexity, vol. 2021, Article ID 8857075, 13 pages, https://doi.org/10.1155/2021/8857075, 2021, Impact factor – 2.680.

9. Haikong Lu, Karthikeyan Rajagopal, FahimehNazarimehr, Sajad Jafari, “A new multi-scroll megastable oscillator based on sign function. International Journal of Bifurcation and Chaos”, Accepted and in press, 2021, Impact factor – 2.145.

10. Ran Wang, Chun-Biao Li, Serdar Çiçek, Karthikeyan Rajagopal, Xin Zhang, “A memristive hyperjerk chaotic system: amplitude control, FPGA design and prediction with artificial neural network”, Complexity, vol. 2021, Article ID 6636813, 17 pages, https://doi.org/10.1155/2021/6636813, 2021, Impact factor – 2.680.

11. Anitha Karthikeyan, Murat Erhan Cimen, Akif Akgul, Ali Fuat Boz, Karthikeyan Rajagopal, “Persistence and coexistence of infinite attractors in a fractal Josephson junction resonator with unharmonic current phase relation considering feedback flux effect”, Nonlinear Dyn, 103(9B), https://doi.org/10.1007/s11071-020-06159-4, 2021, Impact factor – 4.867.

12. Anitha Karthikeyan, Serdar Cicek, Karthikeyan Rajagopal, Prakash Duraisamy, Ashokkumar Srinivasan, “New hyperchaotic system with single nonlinearity, its electronic circuit and encryption design based on current conveyor”, Turk J Elec Eng& Comp Sci, doi:10.3906, 2021, Impact factor – 0.682.

13. Balamurali Ramakrishnan, Ramesh Ramamoorthy, Chunbiao Li, Akif Akgul, Karthikeyan Rajagopal, “Spiral waves in a lattice array of Josephson junction chaotic oscillators with flux effects, Mathematical Problems in Engineering”, Volume 2021, Article ID 8848914, 9 pages https://doi.org/10.1155/2021/8848914, Impact factor – 1.009.

14. Christos K Volos , Sajad Jafari,  Jesus M Munoz-Pacheco, Jacques Kengne, Karthikeyan Rajagopal, “Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-Excited Attractors-II”, Entropy, 22(12), 1428; DOI: 10.3390/e22121428, 2020 (Editorial) Impact factor – 2.494.

15. Karthikeyan Rajagopal, FahimehNazarimehr, Anitha Karthikeyan, Ashokkumar Srinivasan, Sajad Jafari, CAMO: Self-excited and hidden chaotic flows, International Journal of Bifurcation and Chaos, Vol. 29, No. 11, 1950143 (2019), Impact factor – 2.145.

16. Karthikeyan Rajagopal, Sajad Jafari,SezginKacar, Anitha Karthikeyan, Akif Akgul, Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications, Information Technology Journal, Vol 48, No 1 (2019), Impact factor – 0.8.

17. Karthikeyan Rajagopal, Sajad Jafari, Akif Akgul and Anitha Karthikeyan “Modified jerk system with self-exciting and hidden flows and the effect of time delays on existence of multi-stability”, Nonlinear Dyn 93, 1087–1108 (2018). https://doi.org/10.1007/s11071-018-4247-5, Impact factor – 4.604.

18. Karthikeyan, A., Rajagopal K., Mathew, D. “Fractional order nonlinear variable speed and current regulation of a permanent magnet synchronous generator wind turbine system,” Alexandria Engineering Journal (Elsevier), Vol 57(1), 159 – 167, 2018, DOI: 10.1016/j.aej.2016.10.003, Impact Factor-3.696.

19. Rajagopal K., Karthikeyan, A., Srinivasan, “Complex novel 4D memristor hyperchaotic system and its synchronization using adaptive sliding mode control”, Alexandria Engineering Journal, (Elsevier), https://doi.org/10.1016/j.aej.2017.01.044, 2017.Impact Factor-3.696.

20. Rajagopal K., Vaidyanathan, S., Karthikeyan, A., Duraisamy, P. “Dynamic analysis and Chaos suppression in a Fractional order Brushless DC motor,” Electrical Engineering (Springer), DOI: 10.1007/s00202-016-0444-8, Volume 99, Issue 2, pp 721–733, 2017.Impact factor – 1.296.

21. Rajagopal K., Karthikeyan, A., Srinivasan, A.K. “FPGA implementation of novel fractional order chaotic systems with two equilibriums and no equilibrium and its adaptive sliding mode synchronization” , Nonlinear Dynamics and Chaos in Engineering systems (Springer), Volume 87, Issue 4, page 2281 – 2304, https://doi.org/10.1007/s11071-016-3189-z, 2017.Impact factor – 4.604.

22. Rajagopal K., Laarem, G., Vaidyanathan, S., Karthikeyan, A., Srinivasan, A.K. “Dynamical analysis and FPGA implementation of a novel hyperchaotic system and its synchronization using Adaptive Sliding mode control and genetically optimized PID control,” Mathematical Problems in Engineering (Hindawi), Article ID 7307452, 14 pages, https://doi.org/10.1155/2017/7307452, 2017. Impact factor – 1.179.

23. Rajagopal K., Karthikeyan, A., Duraisamy, P. “Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems,” Nonlinear Engineering, DE GRUYTER, Volume 6, Issue 2,  https://doi.org/10.1515/nleng-2016-0059, 2016.(SNIF-0.439)

24. Rajagopal K., Karthikeyan, A., Duraisamy, P.“Chaos Suppression in Fractional Order Permanent Magnet Synchronous Motor and PI controlled Induction motor by Extended Back stepping Control,” Nonlinear Engineering, DE GRUYTER, Volume 5, Issue 4,  https://doi.org/10.1515/nleng-2016-0036, 2016.(SNIF-0.439).

25. Rajagopal K., Karthikeyan, A. “Chaos suppression of Fractional order Willamowski–Rössler Chemical system and its synchronization using Sliding Mode Control,”Nonlinear Engineering Volume 5, Issue 3, Pages 177–183, DOI: https://doi.org/10.1515/nleng-2016-0027, 2016.(SNIF-0.439).

List of Visiting Scientists

S. No Name Organisation State / Country
1 Dr.Sajad Jafari, Health Research Institute, Amirkabir University of Technology Iran
2 Dr.Irene Moroz Mathematical Institute,University of Oxford  UK
3 Dr.Akif Akgul, Sakarya University Turkey
4 Dr.Chunbiao Li Nanjing University of Information Science & Technology China
5 Dr. Kengne Jacques, University of Dschang Cameroon
6 Dr. Viet-Thanh Pham Hanoi University of Technology Vietnam
7 Dr. Sifeu Takougang Kingni, University of Yaoundé I Cameroon
8 Dr.Shaobo He Central South University China
9 Dr.Zhouchao Wei China University of Geosciences China
10 Dr.Yesgat Admassu, Institute for Research and Development, Ministry of Defence Ethiopia

Center Members

Name Position
Dr.Balamurali Ramakrishnan  Director
Dr. Karthikeyan Rajagopal Senior Research Faculty
Prakash. D Research Faculty
Ashokkumar. S Research Faculty
Sampath. T Research Faculty
Vikram. R Research Faculty

Collaborating Researchers from