Sishu Shankar Muni


Assistant Professor

Specializations: Nonlinear dynamics, Bifurcation theory, Linear Algebra, Numerical methods, Differential Equations, Number theory 

Research field: Nonlinear dynamics & chaos, bifurcation theory, neurodynamics, network of oscillators 

Sishu Shankar Muni currently holds the position of Assistant Professor, School of Digital Sciences, Digital University Kerala. Dr. Muni completed his Integrated M. Sc. in applied Mathematics from the National Institute of Technology Rourkela. During his Bachelor studies, he came across a TED talk by Late Prof. Mandelbrot on fractals. Motivated, he started his journey to self learn dynamical systems. After being awarded a doctoral scholarship, he moved to Massey University, New Zealand to pursue his Ph.D. research in applied mathematics, specifically on dynamical systems. He then decided to work on a challenging conjecture during his postdoc at the Indian Institute of Science Education and Research Kolkata. After the successful postdoc, he joined the School of Digital Sciences, Digital University Kerala as an Assistant Professor. Dr. Muni is motivated to do research on nonlinear dynamical systems which are ubiquitous in nature. These systems exhibit striking complicated dynamics. The research involves the use of both computer simulations and mathematics to understand these complicated behaviors. Recently, Dr. Muni started applying his ideas of dynamical systems to neuroscience, power electronic systems, and mathematical biology.

Dr. Muni is fascinated about dynamical systems. Simple nonlinear dynamical systems can exhibit striking complicated behaviors such as sensitive dependence to initial conditions popularly known as “butterfly effect” and chaos (in mathematical terms). Dr. Muni investigates a deeper understanding of these systems. His research works are classified as follows :
1. Explore different bifurcations in two and three dimensional mappings.
2. Understanding the behavior of network of dynamical systems.
3. Application of various techniques of dynamical systems to neuroscience, biological models, and electronic systems.
4. Application of machine learning techniques to open problems of dynamical systems


• Funding award from International Society of Discrete dynamics 2023
• Funding award from International Society of Discrete dynamics 2022
• Post doctoral Fellowship from IISER Kolkata 2022
• School of Fundamental Sciences doctoral bursary scholarship award 2021
• Massey University doctoral scholarship 2018-2021
• SMB registration fellowship 2021
• SIAM travel award 2021
• NZMS travel award 2020
• ANZIAM travel award 2019
• Kalman Summer scholarship 2019
• Gold medal for academic excellence from NIT, Rourkela 2018
• Topper of integrated M.Sc. mathematics, NIT, Rourkela 2018
• Santa Fe Institute MOOC scholarship 2018
• S.N Bhatt memorial excellence fellow at International Centre for Theoretical Sciences 2017
• Summer research fellow of Indian Academy of Sciences 2016
• Annual SBI scholarship 2014-2018


0. S.S. Muni, Ergodic and resonant torus doubling bifurcation in a three-dimensional quadratic map, Nonlinear Dynamics, Springer Nature,, 2024

1. S.S. Muni, S. Banerjee. Bifurcations of mode-locked periodic orbits in three-dimensional maps,
International Journal of Bifurcation and Chaos,33(10):2330025, 2023.
2. S.S. Muni. Mode-locked orbits, doubling of invariant curves in discrete Hindmarsh-Rose neuron
model, Physica Scripta, 98: 085205, 2023.
3. S.S. Muni, R.I. McLachlan, D.J.W. Simpson. Unfolding globally resonant homoclinic tangencies,
Discrete Continuous Dynamical Systems Series A, 42(8): 4013-4030, 2022.
4. S.S. Muni, H. O. Fatoyinbo, I. Ghosh. Dynamical effects of electromagnetic flux on Chialvo
neuron map: nodal and network behaviors, International Journal of Bifurcation and Chaos, 32(9):
2230020, 2022.
5. S.S. Muni, R.I. McLachlan, and D.J.W. Simpson. Homoclinic tangencies with infinitely many
asymptotically stable single-round periodic solutions, Discrete Continuous Dynamical Systems
Series A, 41(8), 3629-3650, 2021.
6. S.S. Muni and A. Provata. Chimera states in ring–star network of Chua circuits. Nonlinear
Dynamics, 101 (4), 2509-2521, 2020.
7. V. Santos, M. Sales, S.S. Muni, J.D. Szezech Jr, A. M. Batista, S. Yanchuk, J. Kurths. Iden-
tification of single-and double-well coherence-incoherence patterns by the binary distance matrix,
Communications in Nonlinear Science and Numerical Simulation, 1007-5704, 2023.
8. A.V. Bukh, I.A. Shepelev, E.M. Elizarov, S.S. Muni, E. Sch ̈oll, G.I. Strelkova. Role of coupling
delay in oscillatory activity in autonomous networks of excitable neurons with dissipation,Chaos,
9. I. Ghosh, S.S. Muni, H.O. Fatoyinbo. On the analysis of a heterogeneous coupled network of
memristive Chialvo neurons, Nonlinear Dynamics, 2023.
10. I.A. Shepelev, A.V. Bukh, S.S. Muni, V.S. Anishchenko. Role of solitary states in forming
spatiotemporal patterns in a 2D lattice of van der Pol oscillators. Chaos Solitons & Fractals, 135,
109725(3), 2020.
11. Z.T. Njitacke, S.S. Muni, S. Seth, J. Awrejcewicz, J. Kengne. Complex dynamics of a heteroge-
neous network of Hindmarsh Rose neurons, Physica Scripta, 98(4), 2023.
12. E. Rybalova, S.S. Muni, and G. Strelkova, Transition from chimera/solitary states to traveling
waves, Chaos, 33, 033104, 2023.
13. S. Kanagaraj, S.S. Muni, A. Karthikeyan, R. Karthikeyan. A chaotic Hartley oscillator with
fractional-order JFET and its network behaviors, Eur. Phys. J. Spec. Top., 98: 085205, 2023.
14. S.S. Muni, Z. T. Njitacke, C. Feudjio, T.F. Fozin, J. Awrejcewicz. Route to chaos and chimera
states in a network of memristive Hindmarsh-Rose neurons model with external excitation. Chaos
Theory and Applications, 4(3): 119-127, 2022.
15. Z.N. Tabekoueng, S.S. Muni, T.F. Fozin, G.D. Leutcho, J. Awrejcewicz. Coexistence of in-
finitely many patterns and their control in heterogeneous coupled neurons through a multistable
memristive synapse, Chaos, 32, 053114, 2022.
16. L.K. Kengne, S.S. Muni, J. C. Chedjou, K. Kyandoghere. Various coexisting attractors, asymme-
try analysis and multistability control in a 3D memristive Jerk system, European Physical Journal
Plus, 137, 848, 2022.
17. Z.N. Tabekoueng, T.F. Fozin, S.S. Muni, J. Awrejcewicz, J. Kengne. Energy computation,
infinitely coexisting patterns and their control from a Hindmarsh-Rose neuron with memristive
autapse: circuit implementation, International Journal of Electronics and Communications Else-
vier, 155, 154361, 2022.
18. I.A. Shepelev, S.S. Muni, E. Sch ̈oll, G.I. Strelkova. Repulsive inter-layer coupling induces anti-
phase synchronization, Chaos, 31, 063116, 2021.
19. I.A. Shepelev, S.S. Muni, T.E. Vadivasova. Synchronization of wave structures in a heterogeneous
multiplex network of 2D lattices with attractive and repulsive intra-layer coupling, Chaos, 31,
021104, 2021.
20. I.A. Shepelev, S.S. Muni, T.E. Vadivasova. Spatiotemporal patterns in a 2D lattice with linear
repulsive and nonlinear attractive coupling. Chaos, 31 (4), 043136, 2021.
21. S.S. Muni, K. Rajagopal, A. Karthikeyan, S. Arun. Discrete hybrid Izhikevich neuron model:
nodal and network behaviours considering electromagnetic flux coupling, Chaos, Solitons and
Fractals, 155, 111759, 2021.
22. H.O. Fatoyinbo, S.S. Muni, A. Abidemi Influence of Sodium Inward Current on Dynamical
Behaviour of Modified Morris-Lecar Model, European Physical Journal B, 95(4), 2021.
23. I.A. Shepelev, A.V. Bukh, S.S. Muni, V.S. Anishchenko. Quantifying the transition from spiral
waves to spiral wave chimeras in a lattice of self-sustained oscillators. Regular Chaotic Dynamics,
25, 597–615, 2020.

1) National conference on contemporary progress in Mathematics, IN October, 2023
 – From Homoclinic tangencies to stable periodic solutions
2) International Conference on Nonlinear Science and Applications, IN October, 2023
 –  Resonant torus doubling bifurcations
3) International Conference on Discrete Equations and Applications, Thailand July, 2023
 – Doubling bifurcation of mode-locked orbits in 3D maps
 – On nested multi-band closed invariant curves in non-smooth systems (special session)
4) Conference on Nonlinear System Dynamics, IN Dec, 2022, IISER Pune
5) NCM workshop on control theory and differential equations, IN Nov, 2022, IISER Kolkata
6) International Conference on Discrete Equations and Applications, FR July, 2022 (Online mode)
7) Mid year ANZIAM meeting 2022 July, 2022 (Online mode)
8) ANZIAM Conference 2022 Feb, 2022 (Online mode)

9) Manawatu Wellington Applied Math Conference 2021 Dec, 2021 (Online mode)
10) New Zealand Mathematical Society conference 2021 Dec, 2021 (Online mode)
11) SIAM Dynamical Systems conference 2021 May, 2021 (Online mode)
12) Dynamical systems in NZ November, 2021
     – Unfolding globally resonant homoclinic tangencies
14) Dynamics days 2021 August, 2021 (Online mode)
     – Globally Resonant Homoclinic Tangencies
15) Society of Mathematical Biology June, 2021 (Online mode)
     – Dynamics of discretised Izhikevich neuron model
16) NeSI community of practice May, 2021, Massey University, NZ
17) Cluster computing: From networks of coupled oscillators to chimera states,ANZIAM conference February, 2021, Australia, AU
     –  From homoclinic tangencies to stable periodic solutions
18) Wellington Manawatu Applied Mathematics conference October, 2020, Victoria University of Wellington, NZ
     – From homoclinic tangencies to stable periodic solutions
19) 3MT colloquium July, 2020, Massey University, NZ
   –  Attractors around us
20) ANZIAM conference February, 2020, Hunter valley, AU
   – A new geometric mechanism of multistability in smooth dynamical systems
21) NZMS colloquium November, 2019, Massey University, NZ
  –  A new geometric mechanism of multistability in smooth dynamical systems
22) NZMASP conference November, 2019, University of Cantebury, NZ
  –  Unfolding balanced homoclinic tangencies
23) SCEECS IEEE international student conference August, 2018, National Institute of Technology, IN
  –   A study on the synchronization aspect of star connected identical Chua circuits
24) ICTS Summer talks July, 2017, International Centre for Theoretical Science, IN
  –  Nonlinear dynamics of a simplified monsoon model
Reviewer for Nature: Scientific Reports., Nonlinear Dynamics, Springer, AIP:Chaos, International Journal of Bifurcation and Chaos, World Scientific, Journal of Computational Science, Elsevier, International Journal of Modern Physics B., World Scientific, International Journal of Dynamics and Control, Frontiers in Physiology
• Invited speaker at a national conference organized by Berhampur University, 2023.
• Invited presenter at Indian Institute of Science Education and Research, Kolkata, 2022.
Invited talk at the Colloquium on “Recent trends of social ethics in science and technology”
organized by Berhampur University, 2022.
Invited talk on “From homoclinic tangencies to stable periodic solutions” at WMAM 2020 organized by Victoria University of Wellington