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Journal of Applied Nonlinear Dynamics 15(1) (2026) 235--244 | DOI:10.5890/JAND.2026.03.013

Pushali Trikha$^1$, Lone Seth Jahanzaib$^2$, Mudassir Ahmad$^1$

$^1$ Department of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Punjab 144001, India

$^2$ Department of Mathematical Sciences, Islamic University of Science and Technology, Awantipora Pulwama, Jammu and Kashmir, India

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Abstract

Considering the increasing virus spread in the society, it is important to understand the connection between respiratory illnesses, the prevalence of respiratory viruses, and meteorological conditions in various nations in order to effectively prepare hospital services for admissions. The paper addresses the fractional four dimensional chaotic system predicting respiratory diseases. The system is thoroughly analyzed by using dynamical tools of phase portraits, bifurcation diagrams, Lyapunov diagrams etc. Adaptive SMC method is applied for controlling chaos in presence of uncertainties and disturbances. Theoretical studies is verified numerically using MATLAB.

References

1. [1]	Kuhfittig, P.K.F. and Davis, T.W. (1990), Predicting the unpredictable.

2. [2]	Gleick, J. (1987), The butterfly effect, Chaos: Making a New Science, 9-32.

3. [3]

   Holbrook, M.B. (2003), Adventures in complexity: an essay on dynamic open complex adaptive systems, butterfly effects, self-organizing order, coevolution, the ecological perspective, fitness landscapes, market spaces, emergent beauty at the edge of chaos, and all that jazz, Academy of Marketing Science Review, (6), 1-184.

4. [4]	Baleanu, D., Jajarmi, A., Mohammadi, H., and Rezapour, S. (2020), A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative, Chaos, Solitons $\&$ Fractals, 134, 109705.

5. [5]	Inan, B., Osman, M.S., Ak, T., and Baleanu, D. (2019), Analytical and numerical solutions of mathematical biology models: the Newell-Whitehead-Segel and Allen-Cahn equations, Mathematical Methods in the Applied Sciences, Wiley Online Library.

6. [6]	van der Pol, B. and van der Mark, J. (1927), Frequency demultiplication, Nature, 120, 363-364.

7. [7]	Kia, B. (2011), Chaos computing: from theory to application, Technical report, Arizona State University.

8. [8]	Ditto, W. and Munakata, T. (1995), Principles and applications of chaotic systems, Communications of the ACM, 38, 96-102.

9. [9]	Ayres, J., Forsberg, B., Annesi-Maesano, I., Dey, R., Ebi, K., and others (2009), Climate change and respiratory disease: European respiratory society position statement, European Respiratory Journal, 34, 295-302.

10. [10]	Joshi, M., Goraya, H., Joshi, A., and Bartter, T. (2020), Climate change and respiratory diseases: A 2020 perspective, Current Opinion in Pulmonary Medicine, 26, 119-127.

11. [11]	Tavassoli, M.H., Tavassoli, A., and Rahimi, M.R.O. (2013), The geometric and physical interpretation of fractional order derivatives of polynomial functions, Differential Geometry-Dynamical Systems, 15, 93-104.

12. [12]	Khan, A., Lone, S.J., and Trikha, P. (2019), Analysis of a novel 3-D fractional order chaotic system, Proceedings of the International Conference on Power Electronics, Control and Automation (ICPECA), 1-6.

13. [13]	Volos, C.K., Kyprianidis, I.M., and Stouboulos, I.N. (2013), Image encryption process based on chaotic synchronization phenomena, Signal Processing, 93(5), 1328-1340.

14. [14]	Geist, K., Parlitz, U., and Lauterborn, W. (1990), Comparison of different methods for computing Lyapunov exponents, Progress of Theoretical Physics, 83(5), 875-893.

15. [15]	Trikha, P. and Jahanzaib, L.S. (2020), Dynamical analysis of a novel 5-D hyper-chaotic system with no equilibrium point and its application in secure communication, Differential Geometry-Dynamical Systems, 22, 269-288.

16. [16]	Javidi, M. and Nyamoradi, N. (2013), Dynamic analysis of a fractional order prey-predator interaction with harvesting, Applied Mathematical Modelling, 37(20-21), 8946-8956.

17. [17]	Wang, Z., Sun, Y., and Cang, S. (2011), A 3-D spherical attractor.

18. [18]	Yu, S., Lu, J., and Chen, G. (2007), Multifolded torus chaotic attractors: design and implementation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 17(1), 013118.

19. [19]	Zhang, S., Zeng, Y., and Li, Z. (2018), One to four-wing chaotic attractors coined from a novel 3-D fractional-order chaotic system with complex dynamics, Chinese Journal of Physics, 56(3), 793-806.

20. [20]	Chua, L., Komuro, M., and Matsumoto, T. (1986), The double scroll family, IEEE Transactions on Circuits and Systems, 33(11), 1072-1118.

21. [21]	Grassi, G., Severance, F.L., and Miller, D.A. (2009), Multi-wing hyperchaotic attractors from coupled Lorenz systems, Chaos, Solitons $\&$ Fractals, 41(1), 284-291.

22. [22]	Mansour, M., Donmez, T.B., Kutlu, M., and Freeman, C. (2023), Respiratory diseases prediction from a novel chaotic system, 5(1), 20-26.

23. [23]	Matignon, D. (1996), Stability results for fractional differential equations with applications to control processing, Computational Engineering in Systems Applications, 2, 963-968, IMACS, IEEE-SMC, Lille, France.

24. [24]	Vidyasagar, M. (2002), Nonlinear Systems Analysis, 42, SIAM.