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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:

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

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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.


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