Sishu Shankar Muni

Contact: sishu.shankar@duk.ac.in

Google Scholar: https://scholar.google.com/citations?user=HqDJFc0AAAAJ&hl=en

Personal webpage: sites.google.com/view/phenosis

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

Research field: Nonlinear Dynamics & Chaos, Bifurcation Theory, Computational Neuroscience, Network of Oscillators, Reservoir Computing, Population Dynamics, Ecological Dynamics

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

• Top 2% Scientist list 2025 in Stanford University list, Elsevier
• Editor of scientific journal: Franklin Open, Elsevier
• Reviewer for peer-reviewed international journals (SCI indexed): Royal Society of Philosophical Transactions, Chaos, Solitons and Fractals, 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, Journal of Control, Automation and Electrical Systems, Qualitative Theory of Dynamical Systems, Physica Scripta.
• 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

1. H. Baranwal, A.K.B. Chand, S.S. Muni, On Taylor Series Expansion for Discrete Systems Involving     Exponential Function and Assessing Their Chaotic Strength, International Journal of Applied and Computational Mathematics, 12(1), 11, 2026.
2. M. Galchenko, V. Sheptunova, A. Karimov, E. Kopets, S. S. Muni, D. Butusov, New Approaches to Stability Analysis for Semi-Implicit Numerical Integration Methods, Mathematics, 14(2), 231,2026.
3. S.S. Muni, Conjoined Lorenz twin attractors in 3D sinusoidal map, Chaos, Solitons and Fractals, 2026.
4. S.S. Muni, Robust chaos in generalized ceil map, Chaos, Solitons and Fractals, 2026.
5. S.S. Muni, Complexity of coexistence regions in the GRHT map, International Journal of Bifurcation and Chaos, (2025).
6. S.S. Muni, Discrete Lorenz attractors in 3D sinusoidal maps, International Journal of Bifurcation and Chaos, (2025).
7. S.S. Muni, Torus and Hyperchaos in three-dimensional Lotka-Volterra map. International Journal of Bifurcation and Chaos, 35, 03 (2025).
8. S.S. Muni, Discontinuous-like periodic transitions and coexistence of mode-locked orbits in delayed Moran-Ricker map, International Journal of Dynamics and Control, 13(5), 198, (2025).
9. W. Tikjha, S.S. Muni, Explicit 2-cycle solutions and bifurcation structures in a non-invertible planar rational map. Int. J. Dynamics and Control 13, 184 (2025).
10. I. Ghosh, H.O. Fatoyinbo, S.S. Muni, Time series analysis of coupled slow–fast neuron models: From Hurst exponent to Granger causality, Chaos, 35, (2025).
11. I. Ghosh, H.O. Fatoyinbo, S.S. Muni, Comprehensive analysis of slow-fast denatured Morris-Lecar neurons, Physical Review E, 111, 044204, 2025.
12. Vismaya V S, S.S. Muni, A.K. Panda, B Mondal, Degn–Harrison map: Dynamical and network behaviours with applications in image encryption, Chaos, Solitons & Fractals, 192, 115987, 2025.
13. E Rybalova, A Ryabov, S.S. Muni, G Strelkova, Coherence-resonance patterning in neural map networks under Gaussian and L´evy noise, The European Physical Journal Special Topics, 1-12, 2025.
14. Joelson D. V. Hermes, Matheus Hansen, Sishu S. Muni, Edson D. Leonel, Iberˆe Luiz Caldas, Analysis of invariant spanning curves in oval billiards: A numerical approach based on Slater’s theorem, Chaos: AIP, 35, 033132,2025.
15. B Mondal, P Majumdar, A Sarkar, SS Muni, Chaos to stability: the role of memory in tri-trophic food chain dynamics, Journal of Applied Mathematics and Computing, 72 (1), 38, 2025
16. P Swetha, JS Ram, DS Varghese, AS Nair, AM Suresh, C Davis, CR Remya, AS Abhirami, A Hareendran, N Fathima, SS Muni, AV Bukh, The influence of L´evy noise and delay on the spiral waves in one and two-dimensional lattices of coupled Chialvo neurons, Chaos, Solitons & Fractals, 202, 117523, 2025
17. Harisankar R., Abhishek Kaushik, Sishu Shankar Muni, Path planning for multi-quadrotor 3D boundary surveillance using non-autonomous discrete memristor hyperchaotic system, Franklin Open,100239, 2025.
18. S.S. Muni, Ergodic and resonant torus doubling bifurcation in a three-dimensional quadratic map, Nonlinear Dynamics, Springer Nature, http://dx.doi.org/10.1007/s11071-024-09284-6, 2024.
19. G.M. Ramırez- Avila, S.S. Muni, T. Kapitaniak, Unfolding the distribution of periodicity regions and diversity of chaotic attractors in the Chialvo neuron map, Chaos (Editors Pick), 34(8), 2024.
20. J.S. Ram, S.S. Muni, I.A. Shepelev, Spatiotemporal patterns in a 2D lattice of Hindmarsh-Rose neurons induced by high-amplitude pulses, Chaos Solitons & Fractals, 189(1), 2024.
21. S.S. Muni, Pathways to hyperchaos in a three-dimensional quadratic map. Eur. Phys. J. Plus 139, 636 (2024).
22. I.D. Kolesnikov, A.V. Bukh, S.S. Muni, J.S. Ram, Impact of L´evy noise on spiral waves in a lattice of Chialvo neuron map, Chaos, Solitons & Fractals, 190, 115759, 2024.
23. T.Haridas, Upasana S.D., Vyshnavi G., M. S. Krishnan, S. S. Muni, Chaos-based audio encryption: Efficacy of 2D and 3D hyperchaotic systems, Franklin Open, 8, 2024.
24. A. S. Nair, I. Ghosh, H. O. Fatoyinbo, S. S. Muni, On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings, Chaos, 2024 (Accepted), DOI: 10.1063/5.0217017.
25. E. Rybalova, A. Ryabov, S.S. Muni, G. Strelkova, L´evy Noise-Induced Coherence Resonance in Neural Maps, Chaos, Solitons, and Fractals, 2024, https://doi.org/10.1016/j.chaos.2024.115210.
26. Vismaya V S, B.V. Nair, S.S. Muni, Deep learning for prediction and classifying the dynamical behaviour of piecewise-smooth maps, Franklin Open, 100180 , 2024.
27. K Srinivasan, G Sivaganesh, TF Fozin, RG Pradeep, SS Muni, Symmetry, chaos control and hysteresis in a second-order non-autonomous circuit with square-wave excitation, The European Physical Journal Plus 139 (11), 1-16.
28. Soula, Y., S.S. Muni, Ouahabi, R. Dynamical behavior and bifurcations in a two-dimensional discrete chaotic system with a rational fraction. J. Appl. Math. Comput. (2024).https://doi.org/10.1007/s12190-024-02315-w.
29. BF Boui A Boya, S.S. Muni, JL Echenausıa-Monroy, J Kengne, Chaos, synchronization, and emergent behaviors in memristive hopfield networks: bi-neuron and regular topology analysis, The European Physical Journal Special Topics, 1-15, 2024.
30. S.S. Muni, Unstable periodic orbits and hyperchaos in 2D quadratic memristor map. Franklin Open, 100193 (2024).
31. I. Ghosh, A.S. Nair, H.O. Fatoyinbo, S.S. Muni. Dynamical properties of a small heterogeneous chain network of neurons in discrete time. Eur. Phys. J. Plus, 139, 545 (2024).
32. J.L. Echenausıa-Monroy, R.C. Garcıa, H.E.G. Velazquez, S.S. Muni, J.Alvarez-Gallegos, Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties, Chaos Theory and Applications, 6(2), 73-82, https://doi.org/10.51537/chaos.1376123, 2024.
33. D. Mukherjee, S.S. Muni, H.O. Fatoyinbo, A dynamical system framework for a mathematical model of atherosclerosis, Franklin Open, 100116, 2024.
34. Srinivasan, K., Sivaganesh, G., Fozin, T.F., R. G. Pradeep, S.S. Muni, Symmetry, chaos control and hysteresis in a second-order non-autonomous circuit with square-wave excitation. Eur. Phys. J. Plus 139, 985 (2024).
35. Vismaya V.S., B.V. Nair, S.S. Muni, Deep learning for prediction and classifying the dynamical behaviour of piecewise-smooth maps, Franklin Open, 100180, (2024).
36. 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.
37. S.S. Muni. Mode-locked orbits, doubling of invariant curves in discrete Hindmarsh-Rose neuron model, Physica Scripta, 98: 085205, 2023.
38. V. Santos, M. Sales, S.S. Muni, J.D. Szezech Jr, A. M. Batista, S. Yanchuk, J. Kurths. Identification of single-and double-well coherence-incoherence patterns by the binary distance matrix, Communications in Nonlinear Science and Numerical Simulation, 1007-5704, 2023.
39. 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, 33(7),2023.
40. I. Ghosh, S.S. Muni, H.O. Fatoyinbo. On the analysis of a heterogeneous coupled network of memristive Chialvo neurons, Nonlinear Dynamics, 2023.
41. Z.T. Njitacke, S.S. Muni, S. Seth, J. Awrejcewicz, J. Kengne. Complex dynamics of a heterogeneous network of Hindmarsh Rose neurons, Physica Scripta, 98(4), 2023.
42. E. Rybalova, S.S. Muni, and G. Strelkova, Transition from chimera/solitary states to traveling waves, Chaos, 33, 033104, 2023.
43. 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.
44. 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.
45. 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.
46. 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.
47. Z.N. Tabekoueng, S.S. Muni, T.F. Fozin, G.D. Leutcho, J. Awrejcewicz. Coexistence of infinitely many patterns and their control in heterogeneous coupled neurons through a multistable memristive synapse, Chaos, 32, 053114, 2022.
48. L.K. Kengne, S.S. Muni, J. C. Chedjou, K. Kyandoghere. Various coexisting attractors, asymmetry analysis and multistability control in a 3D memristive Jerk system, European Physical Journal Plus, 137, 848, 2022.
49. I.A. Shepelev, S.S. Muni, E. Sch¨oll, G.I. Strelkova. Repulsive inter-layer coupling induces anti-phase synchronization, Chaos, 31, 063116, 2021.
50. 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.
51. 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.
52. 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.
53. 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.
54. 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.
55. S.S. Muni and A. Provata. Chimera states in ring–star network of Chua circuits. Nonlinear Dynamics, 101 (4), 2509-2521, 2020.
56. 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.
57. 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.
13. Dynamics days 2021 August, 2021 (Online mode)
     – Globally Resonant Homoclinic Tangencies.
14. Society of Mathematical Biology June, 2021 (Online mode)
     – Dynamics of discretised Izhikevich neuron model.
15. NeSI community of practice May, 2021, Massey University, NZ                                                                             – Cluster computing: From networks of coupled oscillators to chimera states.
16. ANZIAM conference February, 2021, Australia, AU
     –  From homoclinic tangencies to stable periodic solutions.
17. Wellington Manawatu Applied Mathematics conference October, 2020, Victoria University of Wellington, NZ
     – From homoclinic tangencies to stable periodic solutions.
18. 3MT colloquium July, 2020, Massey University, NZ
      –  Attractors around us.
19. ANZIAM conference February, 2020, Hunter valley, AU
     – A new geometric mechanism of multistability in smooth dynamical systems.
20. NZMS colloquium November, 2019, Massey University, NZ
     –  A new geometric mechanism of multistability in smooth dynamical systems.
21. NZMASP conference November, 2019, University of Cantebury, NZ
     –  Unfolding balanced homoclinic tangencies.
22. SCEECS IEEE international student conference August, 2018, National Institute of Technology, IN
     –   A study on the synchronization aspect of star connected identical Chua circuits.
23. ICTS Summer talks July, 2017, International Centre for Theoretical Science, IN
     –  Nonlinear dynamics of a simplified monsoon model.

1. Invited speaker: Recent Developments in Applied and Computational Mathematics, Jan 2026, IIST, 2026.
2. Invited speaker: International Conference on Discrete Equations and Applications, France & Thailand, 2023
3.  Invited speaker at a national conference organized by Berhampur University, 2023.
4. Invited presenter at Indian Institute of Science Education and Research, Kolkata, 2022.
5. Invited talk at the Colloquium on “Recent trends of social ethics in science and technology”
   organized by Berhampur University, 2022.
6. Invited talk on “From homoclinic tangencies to stable periodic solutions” at WMAM 2020 organized by Victoria University of Wellington.

Ph.D. scholars on roll (Number and broad theme of work)
1) Vismaya V S (253811): Cyclic Periodic Synchronization in PLD mappings. (2025) (Ongoing)

Postdoctoral fellows and research staff:
1) Ms. Gowthami B, Computational Linguistics, Government Engineering College Pallakkad, Internship MTech, 2025, Supervisor: Dr. Sishu Shankar Muni
2) Ms. Sreekutty S, Computational Linguistics, Government Engineering College Pallakkad, Internship MTech, 2025,  Supervisor: Dr. Sishu Shankar Muni

1. Anandik N Anand, M.Sc. Data science and Bio-AI and Sandra Sajeev, M.Sc. Data Analytics and Computational Science, bagged District winner of Young Innovators Programme 6.0 conducted by Kerala Development and Innovation Strategic Council (K-DISC). Idea ID : 51715,                                                                                                                                                                                                                                                      Theme : Problems of the Marginalised and Backward Regions, by YIP (Young Innovators Programme), 2025.

1. UGC-MMTTC Faculty Induction Programme (Guru Dakshta) organized by UGC and Digital University Kerala from 13th January to 08th February, 2025.

2. AICTE FDP certificate for Data Analytics and Cloud Computing

Editorial Roles

• Associate Editor: Franklin Open (Journal of Franklin Institute), Elsevier
• Reviewer: 24 international Q1 journals including Nature Scientific Reports, Nonlinear Dynamics, Chaos, Solitons and Fractals, International Journal of Bifurcation and Chaos

Courses Taught

• Numerical Methods
• Scientific Computing and Computational Techniques
• Computational Nonlinear Dynamics
• Data Analytics & Visualization
• Scientific Writing and Communication

Workshops, conferences, and seminars organized

• Co-organizer of International Conference on Computational Mathematics and its Applications, NIST University, Berhampur City College, Odisha, Feb 2025.
• Resource person in the workshop on Data science conducted by the School of Digital Sciences, Digital University Kerala, Jan-Feb 2025.

Innovation

• Mentored student teams that won the District Winner Award at the Young Innovators Programme 6.0 conducted by the Kerala Development and Innovation Strategic Council (K-DISC).
  Idea ID: 51715 | Theme: Problems of the Marginalised and Backward Regions on SADAS

Sponsored research projects

• NBHM (National Board for Higher Mathematics), DAE, Government of India, funding grant for research project, 2025-2028, Title: Beyond Arnold Tongues: The Role of Extreme Curves, Superstable Curves, and Invariant Manifolds in the Bifurcation Structure of Chaotic Mapping.

Centres of excellence and labs

• Computational Nonlinear Dynamics Lab (CNLD lab) under supervision of Dr. Sishu Shankar Muni

Academic bodies and meetings (internal and external)

1. Visited Allianz, UST as a placement coordinator of SoDS
2. Participated in Board of Studies SoDS meeting
3. Assistant and Chief superintendent of Exam section, COE of the University

Internal quality assurance initiatives

1. Introduced novel 500 level course on Computational Nonlinear Dynamics, Optimization methods for data science for M.Sc. Data Analytics and Computational Science programme.
2. Syllabus revision and member of exam question paper review committee
3. DUAT  2025 exam setter and vetter
4. DRAT  2025  exam setter and vetter
5. Trained M.Sc. and M.Tech students for DACE (Digital Access and Community Empowerment) for SADAS project which won KDISC YIP award.
6. Internship coordinator of SoDS managing 4th semester
7. Supporting faculty member of Dean Research

Learning management systems

• Effective use of Moodle LMS and Google Classroom for conducting examinations, delivering lectures, managing live attendance, administering quizzes, and sharing study materials.
• Regular use of a tablet-enabled teaching approach for real-time explanation and interactive writing during lectures.
• Adoption of a data-driven student feedback Google forms to continuously assess learning outcomes and improve course content and instructional methods.

Digital content creation

• University related chatbot created by Mr. Aman Sharma, DACS, SoDS under supervision of Dr. Sishu Shankar Muni.
• Trained students on LaTeX typesetting skills.

AI/data-driven academic initiatives

• Citation Network Analysis, Turnitin AI detection of student reports and assignments, Mendeley for Literature Review, Bibliography, and Citation Management, experiential and immersive learning using AR-VR.