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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Mechanical Analysis of Burke-Shaw Chaotic System

Discontinuity, Nonlinearity, and Complexity 15(1) (2026) 99--107 | DOI:10.5890/DNC.2026.03.007

Vijay K. Shukla$^{1}$, Arun K. Pandey$^{1}$, Saraswati Acharya$^{2}$, Abhishek Kumar$^{3}$, Neeraj K. Tripathi$^{4}$, Prashant K. Mishra$^{5}$

$^{1}$ Department of Mathematics, Shiv Harsh Kisan P.G. College, Basti-272001, India

$^{2}$ Department of Mathematics, School of Science, Kathmandu University, Dhulikhel, Nepal

$^{3}$ Department of Mathematics, Jai Prakash University, Chapra-841301, India

$^{4}$ Department of Mathematics, Allahabad Degree College, Prayagraj-211003, India

$^{5}$ Department of Mathematics, P. C. Vigyan Mahavidyalaya, Jai Prakash University, Chapra-841301, India

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Abstract

In this article, the mechanic analysis of Burke-Shaw system have been studied. Firstly, the system is transformed into Kolmogorov type system and further decomposed into four types of torques: inertial torque, internal torque, dissipation torque and external torque. Five scenarios are examined using combinations of various torques in order to identify the key elements for chaos creation and their physical significance. In these scenarios, the conversion between kinetic energy, potential energy and Hamiltonian energy are examined. The interaction between energy and the parameters is also explored. The conclusion reveals that any combination of three forms of torques can not create chaos in Burke-Shaw system but a combination of four types of torques concrete it.

Acknowledgments

\bibitem{1} Alvarez, G., Li, S., Montoya, F., Pastor, G., and Romera, M. (2005), Breaking projective chaos synchronization secure communication using filtering and generalized synchronization, \textit{Chaos, Solitons and Fractals}, \textbf{24}, 775-783.

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