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

Call for Fully Sponsored Post graduation

List of Publication

1.      Balamurali Ramakrishnan, Lionel Merveil Anague Tabejieu, Isidore Komofor Ngongiah, Sifeu Takougang kingni, Raoul Thepi Siewe, Karthikeyan Rajagopal,  ”Suppressing chaos in Josephson junction model with coexisting attractors and investigating its collective behavior in a network”, Journal of Superconductivity and Novel Magnetism, Accepted and Inpress, 2021, Impact factor – 1.506.

2.      Karthikeyan Rajagopal, Anitha Karthikeyan, Balamurali Ramakrishnan, “Controlling chaos and supressing chimeras in a fractional order discrete phase locked loop using impulse control”, Chinese Physics-B, Accepted and Inpress, 2021, Impact factor – 1.494.

3.      Nafise Naseri, Sivabalan Ambigapathy, Mohadeseh Shafiei Kafraj, Farnaz Ghasemi, Karthikeyan Rajagopal, Sajad Jafari, “Connecting curves as tools to localize Hidden attractors in a new chaotic hyper-jerk system with no equilibria”, International Journal of Bifurcation and Chaos, Accepted and in press, 2021, Impact factor – 2.836.

4.      Akif Akgül, Karthikeyan Rajagopal, Ali Durdu, Muhammed Ali Pala, Ömer Faruk Boyraz, Mustafa Zahid Yıldız, “A simple fractional-order chaotic system based on memristor and memcapacitor and its synchronization application”, Chaos, Solitons and Fractals, Accepted and Inpress, 2021, Impact factor – 5.944.

5.      Karthikeyan Rajagopal, Sajad Jafari, Anitha Karthikeyan, Ashokkumar Srinivasan, “Effect of magnetic induction on the synchronizability of coupled neuron network”, Chaos 31, 083115, https://doi.org/10.1063/5.0061406, 2021, Impact factor – 3.642.

6.      Lazaros Moysis, Karthikeyan Rajagopal, Aleksandra V. Tutueva, Christos Volos, Beteley Teka, Denis N. Butusov, “Chaotic path planning for 3D area coverage using a pseudo-random bit generator from a 1D chaotic map”, Cognitive Neurodynamics, Accepted and Inpress, 2021, Impact factor – 5.082

7.      Karthikeyan Rajagopal, Prakash Duraisamy, Goitom Tadesse, Christos Volos, Fahimeh Nazarimehr, Iqtadar Hussain, “A fractional-order ship power system: Chaos and its dynamical properties”, International Journal of Nonlinear Sciences and Numerical Simulation (IJNSNS), Accepted and Inpress. Impact factor – 2.007.

8.      Jesus M. Munoz-Pacheco, Christos Volos, Fernando Serrano, Sajad Jafari, Jacques Kengne, Karthikeyan Rajagopal, “Stabilization and Synchronization of a Complex Hidden Attractor Chaotic System by Backstepping Technique”, Entropy, Accepted and Inpress. Impact factor – 2.524.

9.      Sheida Ansari Nasab, Shirin Panahi, Farnaz Ghassemi, Sajad Jafari, Karthikeyan Rajagopal, Dibakar Ghosh, Matjaz Perc, “Functional neuronal networks reveal emotional processing differences in children with ADHD”, Cognitive Neurodynamics, Accepted and Inpress, 2021, Impact factor – 5.082.

10.      Alireza Bahramian, Sajjad Shaukat Jamal, Fatemeh Parastesh, Kartikeyan Rajagopal and Sajad Jafari, The collective behaviors of cortico-thalamic circuits: Logic gates as the thalamus and a dynamical neuronal network as the cortex, Chinese Physics B, Accepted and Inpress, 2021, Impact factor – 1.494.

11.      Janarthanan Ramadoss, Sajedeh Aghababaei, Fatemeh Parastesh, Karthikeyan Rajagopal, Sajad Jafari, Iqtadar Hussain, “Chimera State in the Network of Fractional-Order FitzHugh–Nagumo Neurons”, Complexity, vol. 2021, Article ID 2437737, 9 pages, 2021. https://doi.org/10.1155/2021/2437737. Impact factor – 2.833.

12.      Karthikeyan Rajagopal, Sajad Jafari, Irene Moroz, Anitha Karthikeyan, and Ashokkumar Srinivasan, “Noise induced suppression of spiral waves in a hybrid FitzHugh–Nagumo neuron with discontinuous resetting”, Chaos, Accepted and Inpress, (2021), Impact factor – 3.642, Cite score: 5.6

13.      Ismail Koyuncu, Karthikeyan Rajagopal, Murat Alcin, Anitha Karthikeyan, Murat Tuna,  Metin Varan, “Control, synchronization with linear quadratic regulator method and FFANN-based PRNG application on FPGA of a novel chaotic system”, Eur. Phys. J. Spec. Top. (2021). https://doi.org/10.1140/epjs/s11734-021-00178-x, (2021), Impact factor – 2.707, Cite score: 3.9

14.      Anitha Karthikeyan, Irene Moroz, Karthikeyan Rajagopal, Prakash Duraisamy, “Effect of temperature sensitive ion channels on the single and multilayer network behavior of an excitable media with electromagnetic induction”, Chaos, Solitons and Fractals, Accepted and Inpress, (2021), Impact factor – 5.944, Cite score: 5.9

15.      Karthikeyan Rajagopal, Shirin panahi, Mo Chen, Sajad Jafari, Bocheng Bao, “Suppressing spiral waves turbulence in a simple fractional order discrete neuron map using impulse triggering”, Fractals, https://doi.org/10.1142/S0218348X21400302, (2021),  Impact factor – 3.665, Cite score: 6.3

16.  Fahimeh Nazarimehr, Fatemeh Shahbodaghy, Boshra Hatef, Karthikeyan Rajagopal, “How can we measure the slowing down in healthy and ischemic stroke individuals?”, Scientia Iranica, Accepted and Inpress , (2021),  Impact factor – 1.435, Cite score: 1.5

17.  Karthikeyan Rajagopal, Arthanari Ramesh, Irene Moroz, Prakash Duraisamy, Anitha Karthikeyan, “Local and network behavior of a bistable vibrational energy harvesters considering periodic and quasiperiodic excitations”, Chaos 31, 063111 (2021); https://doi.org/10.1063/5.0054459, (2021), Impact factor – 2.832, Cite score: 5.6

18.  Karthikeyan Rajagopal, Shaobo He, Anitha Karthikeyan , Prakash Duraisamy, “Size matters: Effects of the size of heterogeneity on the wave re-entry and spiral wave formation in an excitable media”, Chaos  31, 053131 (2021); https://doi.org/10.1063/5.0051010, (2021),  Impact factor – 3.642, Cite score: 5.6

19.  Karthikeyan Rajagopal, Shirin Panahi, Zahra Shourgashti, Anitha Karthikeyan , Iqtadar Hussain, “Suppressing spiral waves with delayed asymmetric bidirectional coupling in a multi-layer biological network,” European Physical Journal – Special Topics, Accepted and Inpress, (2021), Impact factor – 2.707, Cite score: 3.9

20.  Adelaide Nicole Kengnou Telem, Karthikeyan Rajagopal, Theophile Fozin Fonzin, Balamurali Ramakrishnan, “On the Dynamics of a System of two Coupled van der Pol Oscillators subjected to a Constant Excitation Force: Effects of Broken Symmetry”, European Physical Journal – Special Topics, Accepted and Inpress, (2021), Impact factor – 2.707, Cite score: 3.9

21.  Karthikeyan Rajagopal, Irene Moroz, Balamurali Ramakrishnan, Anitha Karthikeyan, Prakash Duraisamy, “Modified Morris-Lecar neuron model: Effects of very low frequency electric fields and of magnetic fields on the local and network dynamics of an excitable media”, Nonlinear Dyn  (2021), https://doi.org/10.1007/s11071-021-06494-0, (2021), Impact factor – 5.022, Cite score: 8.7

22.  Karthikeyan Rajagopal, Murat Erhan Cimen, Sajad Jafari, Jay Prakash Singh, Binoy Krishna Roy, Omer Faruk Akmese, Akif Akgul, “A family of circulant megastable chaotic oscillators, its application for the detection of a feeble signal and PID controller for time-delay systems by using chaotic SCA algorithm”, Chaos, Solitons and Fractals, Volume 148, July 2021, 110992, https://doi.org/10.1016/j.chaos.2021.110992, (2021), Impact factor – 5.944, Cite score: 5.9

23.  Changzhi Li, Karthikeyan Rajagopal, Fahimeh Nazarimehr, Yongjian Liu, “A non-autonomous chaotic system with no equilibrium”, Integration, Volume 79, July 2021, Pages 143-156, https://doi.org/10.1016/j.vlsi.2021.04.001, (2021),  Impact factor – 1.211, Cite score: 2.6

24.  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 – 3.642, Cite score: 5.6

25.  Balamurali Ramakrishnan, Irene Moroz, Chunbiao Li, Anitha Karthikeyan, Karthikeyan Rajagopal, “Effects of Noise on the wave propagation in an excitable media with magnetic induction”, Eur. Phys. J. Spec. Top. (2021). https://doi.org/10.1140/epjs/s11734-021-00115-y ,(2021),  Impact factor – 1.660, Cite score: 3.9

26.  M. Mehrabbeik, R. Ramamoorthy, Karthikeyan Rajagopal, F. Nazarimehr, S. Jafari, I. Hussain, “Critical Slowing Down Indicators in Synchronous Period-Doubling for Salamander  Flicker Vision”,  European Physical Journal – Special Topics, Accepted and Inpress, (2021),  Impact factor – 2.707, Cite score: 3.9

27.  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 – 2.833, Cite score: 3.2

28.  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, DOI:10.1007/s12648-021-02075-4, 2021, Impact factor – 1.947, Cite score: 2.2

29.  Karthikeyan Rajagopal, A. Jafari, S. He, F. Parastesh, S. Jafari, I. Hussain, “Simplest symmetric chaotic flows: The strange case of asymmetry in Master Stability Function”, Eur. Phys. J. Spec. Top. (2021). https://doi.org/10.1140/epjs/s11734-021-00131-y, (2021),  Impact factor – 2.707, Cite score: 3.9

30.  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 – 5.944, Cite score: 5.9

31.  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 – 2.713, Cite score: 2.5

32.  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 – 2.833, Cite score: 3.2

33.  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 – 2.836, Cite score: 4.2

34.  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 – 2.833, Cite score: 3.2

35.  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 – 5.022, Cite score: 8.7

36.  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 (2021), 29: 1692 – 1705, doi:10.3906/elk-2005-86, 2021, Impact factor – 0.806, Cite score: 2.1

37.  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 – 1.305, Cite score: 1.8

38.  Hussain, I., Jafari, S., Ghosh, D. et al. “Synchronization and chimeras in a network of photosensitive FitzHugh–Nagumo neurons”, Nonlinear Dyn 104, 2711–2721 (2021). https://doi.org/10.1007/s11071-021-06427-x, 2021, Impact factor – 5.022, Cite score: 8.7

39.  Dhinakaran Veeman, Hayder Natiq, Nadia M. G. Al-Saidi, Karthikeyan Rajagopal, Sajad Jafari and Iqtadar Hussain, “A New Megastable Chaotic Oscillator with Blinking Oscillation terms “, Complexity, 2021, vol. 2021, 1-12, 2021, Impact factor – 2.833, Cite score: 3.2

40.  Kengne, J., Kengne, L.K., Chedjou, J.C. et al. “A simple anti-parallel diodes based chaotic jerk circuit with arcsinh function: theoretical analysis and experimental verification”, Analog Integr Circ Sig Process (2021). https://doi.org/10.1007/s10470-021-01876-1, Impact factor – 1.337, Cite score: 1.35

41.  Motahare Hazrati, Shirin Panahi, Fatemeh Parastesh, Sajad Jafari, Dibakar Ghosh, “Role of links on the structural properties of different network topologies”, EPL (Europhysics Letters), Volume 133, Number 4, (2021), Impact factor – 1.947, Cite score: 2.6

42.  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 – 2.524, Cite score: 3.7

43.  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 – 2.836, Cite score: 4.2

44.  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 – 1.228, Cite score: 1.56

45.  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 – 5.022, Cite score: 8.7

46.  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 – 3.732, Cite score: 5.6

47.  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 – 3.732, Cite score: 5.6

48.  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 – 1.836, Cite score: 1.4

49.  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 – 5.022, Cite score: 8.7

50.  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 – 1.305, Cite score: 1.8

51.  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-0.757), Cite score: 2.3

52.  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-0.757), Cite score: 2.3

53.  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-0.757), Cite score: 2.3

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