Skip Navigation Links
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Chaotic Simulation of Kinesiology of Musculoskeletal Movements

Journal of Applied Nonlinear Dynamics 11(1) (2022) 233--245 | DOI:10.5890/JAND.2022.03.014

Aashima Bangia, Rashmi Bhardwaj

University School of Basic & Applied Sciences (USBAS), Guru Gobind Singh Indraprastha University, Delhi-110078, India

Download Full Text PDF



Kinesiology is defined as the scientific study of human movement. The relation between various musculoskeletal movements can be diversified as physical activities, exercises, postures for health lifestyle. These can be partitioned mutually exclusively into many different ways. Different muscular movements are an asset of physical activities which are planned, structured and sometimes repetitive. The nonlinear differential model determines change in concentration for oxygen during musculoskeletal physical movements based on two major components heart and energy utilized by the Adenosine triphosphate (ATP) molecules using the compartment model of breath function. In this study, model utilizes non-linear model equalities which are with respect to time at constant rate of metabolism. Lyapunov Characteristic Exponents (LCE) measures the relative stability of the system of the equations. Lyapunov exponents are the most direct indicators and quantifiers of deterministic chaos. The mathematical model for three important components: Heart, Lungs and Cells/Tissues in the body is proposed. The model helps to study the impact of musculoskeletal movements on these factors simultaneously with time and also to study how the change in one component influences the changes in other with respect to time. Body consumes oxygen which is proportional to metabolic rate. It is observed that keeping breath function R constant at 20s and varying Q (amount of oxygen in the body) from 8(L/min) to 70 (L/min), the system experiences regular to chaotic behaviour. Further, it is observed that keeping Q as constant at 70 (L/min), chaotic situation can be controlled and the system be transformed to normal state by enhancing breath function. Thus, it is recommended that for extensive musculoskeletal movements of the body and to avoid collapsing, primarily the breath function should be boosted.


G.G.S. Indraprastha University provided financial support and research facilities. Authors declare no conflict of interest.


  1. [1]  Adeniji, A.E., Njah, A.N., Olusola, O.I. (2020), Regional and Seasonal Variation of Chaotic Features in Hourly Solar Radiation Based on Recurrence Quantification Analysis, Journal of Applied Nonlinear Dynamics, 9(2), 175-187.
  2. [2]  Bhardwaj, R., Datta, D., Bhardwaj, R., Bhardwaj, S., Sharma, S.K., and Shehri, M.A. (2020), An apparatus and method with IoT to detect and control temperature change simulation case. Date of Indian Patent Publication: June 26, 2020. Indian Patent Application No. 202011021339.
  3. [3]  Bhardwaj, R. and Datta, D. (2020), Development of Epidemiological Modeling RD{\_}COVID-19 of Coronavirus Infectious Disease and its Numerical Simulation. Accepted as book chapter in Mathematical Modelling and Analysis of Infectious Disease Problems (COVID-19). (Eds.) Praveen Agarwal, Juan J. Nieto, Delfim F.M. Torres. Springer
  4. [4]  Bhardwaj, R. and Datta, D. (2020), Development of a Recommender System Health Mudra Using Blockchain for Prevention of Diabetes. Recommender System with Machine Learning and Artificial Intelligence: Particle Tools and Applications in Medical and Agricultural Domains. (Eds.) SachiNandan Mohanty, Ahmad A Elengar, Srika Jain, Priya Gupta, Jyotirmoy Chatterjee. Wiley & Sons, USA.
  5. [5]  Bhardwaj, R. and Bangia, A. (2020), Dynamical forensic inference for malware in iot-based wireless transmissions. In K. Sharma, M. Makino, G. Shrivastava, & B. Agarwal (Eds.) Forensic Investigations and Risk Management in Mobile and Wireless Communications, 51-79.
  6. [6]  Bangia, A., Bhardwaj, R., and Jayakumar, K.V. (2020), River water quality estimation through Artificial Intelligence conjuncted with Wavelet Decomposition. 979. Numerical Optimization in Engineering and Sciences, 107-123. Springer.
  7. [7]  Bhardwaj, R. and Bangia, A. (2020), Assessment of Stock prices variation using Intelligent Machine Learning Techniques for the prediction of BSE. Advances in Intelligent Systems and Computing (AISC) Volume 979. Numerical Optimization in Engineering and Sciences, Eds: Kacprzyk J, Debashis Dutta and B Mahanty. 107-123.
  8. [8]  Bhardwaj, R. and Bangia, A. (2020), Data Driven Estimation of Novel COVID-19 Transmission Risks through Hybrid Soft-Computing Techniques, Chaos, Soliton and Fractals, 110152.
  9. [9]  Bhardwaj, R. and Datta, D. (2020), Consensus Algorithm, Studies in Big Data, 71, 91-107. Springer.
  10. [10]  Bhardwaj, R. (2019), Nonlinear Time Series Analysis of Environment Pollutants. Mathematical Modeling on Real World Prolems: Interdisciplinary Studies in Applied Mathematics. 71-102. NOVA Publisher, New York, USA.
  11. [11]  Bhardwaj, R. and Bangia, A. (2019), Hybrid fuzzified-PID controller for non-linear control surfaces for DC motor to improve the efficiency of electric battery driven vehicles, International Journal of Recent Technology and Engineering (IJRTE), 8(3), 2561-2568.
  12. [12]  Bhardwaj, R. and Bangia, A. (2019), Dynamic indicator for the prediction of atmospheric pollutants, Asian Journal of Water, Environment and Pollution, 16(4), 39-50.
  13. [13]  Bhardwaj, R. and Bangia, A. (2019), Stock market trend analysis during demonetization using soft-computing techniques. 2018 International Conference on Computing, Power and Communication Technologies (GUCON-2018). IEEE Xplore Digital Library, 696--701.
  14. [14]  Bhardwaj, R. and Bangia, A. (2018), Statistical time series analysis of dynamics of HIV, JNANABHA, Special Issue 48, 22-27.
  15. [15]  Bhardwaj, R. and Bangia, A. (2019), Neuro-fuzzy analysis of demonetization on NSE. In Bansal, J.C., Das, K.N., Nagar, A., Deep, K., & Ojha, A.K (Eds). Advances in Intelligent Systems and Computing (AISC) (ISSN:2194-5357) Springer Proceedings: Soft Computing for Problem Solving (SocPros-2017), 853-861.
  16. [16]  Bhardwaj, R. and Bangia, A. (2016), Complex Dynamics of Meditating Body, Indian Journal of Industrial and Applied Mathematics, 7(2), 106-116.
  17. [17]  Buckley, J.P., Hedge, A., Yates, T., Copeland, R.J., Loosemore, M., Hamer, M., Bradley, G., and Dunstan, D.W. (2015), The sedentary office: A growing case for change towards better health and productivity, British Journal of Sports Medicine, 49, 1357-1362.
  18. [18]  Bhuvaneswari, V. and Balachandran K. (2020), Lower Bound of Blow up Time for Three Species Cooperating Model, Journal of Applied Nonlinear Dynamics, 9(3), 391-400.
  19. [19]  Buman, M.P. and King, A.C. (2010), Exercise as a Treatment to Enhance Sleep, American Journal of Lifestyle Medicine, 4(6), 500-514.
  20. [20]  Cobiaga, R. and Reartes, W. (2020), Dynamic Scenario in HTLV-I Infection, Journal of Applied Nonlinear Dynamics, 9(3), 349-359.
  21. [21]  Costa, A., Costantino, M.L., and Fumero, R. (1992), Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation, Journal of biomedical engineering, 14(5), 385-389.
  22. [22]  Das, H., Shaikh, A.A., and Sarwadi, S. (2020), Mathematical Analysis of an Eco-Epidemic Model with Different Functional Responses of Healthy and Infected Predators on Prey Species, Journal of Applied Nonlinear Dynamics, 9(4), 667-684.
  23. [23]  Dinas, P.C., Koutedakis, Y., and Flouris, A.D. (2011), Effects of exercise and physical activity on depression, Irish Journal of Medical Science, 180(2), 319-325.
  24. [24]  Hasan, M.N, Uddin, M.S., and Biswas, M.H.A. (2020), Interactive E?ects of Disease Transmission on Predator-Prey Model, Journal of Applied Nonlinear Dynamics, 9(3), 401-413.
  25. [25]  Jaisri, G., Dayananda, G., and Saraswathi Hegde, S.C. (2011), Heart rate variability during meditation in Pranic healers, NJIRM, 2(4), 113-116.
  26. [26]  Kaelin Jr, W.G., Ratcliffe, S.P.J., and Semenza G.L. (2019), Out of breath: molecular description of cellular responses to hypoxia -- 2019 Nobel Prize for Physiology or Medicine, Current Science, 117(9), 1418-1419.
  27. [27]  Lajmiri, Z. and Ghaziani, R.K. (2018), Hopf Bifurcation and stability analysis of predator-prey system with Holling type-IV functional response, Journal of Applied Nonlinear Dynamics, 7(4), 337-348.
  28. [28]  Pchelintsev, A.N. (2020), An Accurate Numerical Method and Algorithm for Constructing Solutions of Chaotic Systems, Journal of Applied Nonlinear Dynamics, 9(2), 207-221.
  29. [29]  Teka, W.W., Upadhyay, R.K., and Mondal, A. (2018), Spiking and bursting patterns of fractional-order Izhikevich model, Communications in Nonlinear Science and Numerical Simulation, 56, 161-176.
  30. [30]  Vyas, R. and Nirupma, D. (2002), Effect of meditation on respiratory system, cardiovascular system and lipid profile, Indian Journal of Physiology and Pharmacology, 46(4), 487-491.