Passivity and dissipativity criteria of discrete-time fractional-order fuzzy genetic regulatory networks

Document Type : Research Paper

Authors

1 Departement of Mathematics, Fculty of Sciences of Bizerte, University of Carthage, Bizerte, Tunisia.

2 University of Carthage, Faculty of Sciences of Bizerte, Department of Mathematics, GAMA Laboratory LR21ES10, BP W, 7021 Zarzouna, Bizerte, Tunisia

3 Departement of Mathematics, Faculty of Sciences of Bizerte, University of Carthage, Bizerte, Tunisia.

10.22111/ijfs.2026.53695.9507

Abstract

Genetic Regulatory Networks (GRNs) constitute a key framework for understanding the development and evolutionary dynamics of biological systems. With the rapid progress of DNA microarray technologies, large-scale genome-wide analysis of GRNs has become feasible. In this work, we are investigated the passivity and dissipativity of Fractional-Order Discrete-Time Fuzzy Genetic Regulatory Networks (FODTFGRNs). Embedding fractional-order operators in the discrete-time formulation allows the model to capture memory-dependent and hereditary features of gene regulatory dynamics. Meanwhile, fuzzy logic techniques are introduced to handle parameter ambiguities and nonlinear gene interactions. This integrated modeling strategy leads to a more accurate and practical representation of genetic regulation phenomena encountered in real biological and medical applications. Moreover, a novel passivity lemma tailored to the considered systems is developed through the construction of a suitable Lyapunov functional. Several sufficient criteria guaranteeing passivity and dissipativity are established by combining the Linear Matrix Inequalities (LMIs) framework with Lyapunov functional analysis, the comparison principle, contradiction arguments, various inequality techniques, and the newly developed passivity lemma. Finally, two simulation examples are presented to validate and illustrate the effectiveness of the proposed theoretical results.

Keywords

Main Subjects

References

[1] S. Ai, Y. Zhou, W. Zou, E. Chatterjee, G. Li, J. Shi, J. Zhao, diffMIN: Reconstructing sample-specific differential gene
regulatory networks based on mutual information, IEEE Transactions on Computational Biology and Bioinformatics,
22(4) (2025), 1935-1946. https://doi.org/10.1109/TCBBIO.2025.3576169
[2] C. Aouiti, M. Bessifi, Periodically intermittent control for finite-time synchronization of delayed quaternion-valued
neural networks, Neural Computing and Applications, 33(12) (2021), 6527-6547. https://doi.org/10.1007/ s00521-020-05417-1
[3] C. Aouiti, Q. Hui, H. Jallouli, E. Moulay, Sliding mode control-based fixed-time stabilization and synchronization of
inertial neural networks with time-varying delays, Neural Computing and Applications, 33(18) (2021), 11555-11572.
https://doi.org/10.1007/s00521-021-05833-x
[4] C. Aouiti, Q. Hui, E. Moulay, F. Touati, Global dissipativity of fuzzy genetic regulatory networks with mixed delays,
International Journal of Systems Science, 53(12) (2022), 2644-2663. https://doi.org/10.1080/00207721.2022.
2056653
[5] R. Chen, H. L. Li, H. Liu, H. Jiang, J. Cao, Complete synchronization of discrete-time fractional-order TS fuzzy
complex-valued neural networks with time delays and uncertainties, IEEE Transactions on Fuzzy Systems, 33(3)
(2025), 842-856. https://doi.org/10.1109/TFUZZ.2024.3492011
[6] W. Cheng, W. Zhang, H. Zhang, D. Chen, J. Cao, Quantized projective synchronization of discrete-time fractionalorder
delayed quaternion-valued fuzzy neural networks and its application to image encryption, Asian Journal of
Control, (2025), 1-24. https://doi.org/10.1002/asjc.3840
[7] W. Cheng, W. Zhang, H. Zhang, I. Stamova, J. Cao, Mittag-Leffler synchronization in finite time of fractionalorder
discrete-time quaternion-valued neural networks via quantized control and its application, Mathematics and
Computers in Simulation, 248 (2026), 362-383. https://doi.org/10.1016/j.matcom.2026.04.016
[8] V. Gokulakrishnan, R. Srinivasan, M. S. Ali, A. S. A. Omer, New results on finite-time synchronisation of fractionalorder
fuzzy reaction-diffusion gene regulatory networks with time-varying delays: An adaptive boundary control approach, International Journal of Systems Science, 57(2) (2026), 414-440. https://doi.org/10.1080/00207721.
2025.2504058
[9] W. Gong, T. Duan, Q. Li, M. Xing, Event-triggered synchronisation control of discrete-time complex-valued networks
with mixed delays: A switching approach, Journal of Control and Decision, (2025), 1-16. https://doi.org/10.1080/
23307706.2025.2517345
[10] Y. Gu, H. Wang, Y. Yu, Synchronization for fractional-order discrete-time neural networks with time delays,
Applied Mathematics and Computation, 372 (2020), 124995. https://doi.org/10.1016/j.amc.2019.124995
[11] D. He, H. Wang, Y. Tian, R. E. Precup, Model-free global sliding mode control using adaptive fuzzy system under
constrained input amplitude and rate for mechatronic systems subject to mismatched disturbances, Information
Sciences, 697 (2025), 121769. https://doi.org/10.1016/j.ins.2024.121769
[12] A. Hentout, A. Maoudj, A. Kouider, Shortest path planning and efficient fuzzy logic control of mobile robots in
indoor static and dynamic environments, Romanian Journal of Information Science and Technology, 27(1) (2024),
21-36. https://doi.org/10.59277/ROMJIST.2024.1.02
[13] T. Huang, Y. Guo, C. Zhang, Stability and synchronization control of fractional-order gene regulatory networks
with mixed delays, Computational and Applied Mathematics, 45 (2026), 139. https://doi.org/10.1007/
s40314-025-03515-1
[14] P. Jothiappan, M. Kalidass, Robust passivity analysis of stochastic genetic regulatory networks with levy noise,
International Journal of Control, Automation and Systems, 20(10) (2022), 3241-3251. https://doi.org/10.1007/
s12555-021-0552-8
[15] R. Li, J. Cao, Z. Tu, Passivity and dissipativity-based fuzzy control of quaternion-valued memristive neural networks
on time scales, Cognitive Neurodynamics, 19(1) (2025), 1-14. https://doi.org/10.1007/s11571-025-10300-7
[16] J. Li, H. Dong, Z. Wang, N. Hou, F. E. Alsaadi, On passivity and robust passivity for discrete-time stochastic
neural networks with randomly occurring mixed time delays, Neural Computing and Applications, 31(1) (2019),
65-78. https://doi.org/10.1007/s00521-017-2980-1
[17] J. Liu, H. L. Li, C. Hu, H. Jiang, J. Cao, Complete synchronization of discrete-time fractional-order BAM neural
networks with leakage and discrete delays, Neural Networks, 180 (2024), 106705. https://doi.org/10.1016/j.
neunet.2024.106705
[18] H. Nabil, H. Tayeb, Chaotic behavior in a discrete-time fractional-order Hopfield neural network and its application
in secure communication, Journal of Computational and Applied Mathematics, 474 (2026), 116926. https://doi.
org/10.1016/j.cam.2025.116926
[19] D. Pan, H. Qu, Finite-time boundary synchronization of space-time discretized stochastic fuzzy genetic regulatory
networks with time delays, AIMS Mathematics, 10(2) (2025), 2163-2190. https://doi.org/10.3934/math.2025101
[20] R. E. Precup, A. T. Nguyen, S. Bla˘zi˘c, A survey on fuzzy control for mechatronics applications, International
Journal of Systems Science, 55(4) (2024), 771-813. https://doi.org/10.1080/00207721.2023.2293486
[21] R. E. Precup, S. Preitl, Stability and sensitivity analysis of fuzzy control systems. Mechatronics applications, Acta
Polytechnica Hungarica, 3(1) (2006), 61-76.
[22] X. She, L. Wang, Y. Zhang, Finite-time stability of genetic regulatory networks with nondifferential delays, IEEE
Transactions on Circuits and Systems II: Express Briefs, 70(6) (2023), 2107-2111. https://doi.org/10.1109/
TCSII.2022.3233797
[23] K. Shipra, R. Maurya, S. N. Sharma, Euler-Lagrange passivity-based controller for the three-level ´cuk PFC converter
for electric vehicle battery charging application, International Journal of Control, 96(2) (2023), 408-423. https:
//doi.org/10.1080/00207179.2021.1998637
[24] G. Stamov, I. Stamova, On the practical stability of h-manifolds for impulsive fractional-order gene regulatory
networks, Biomath Communications Supplement, (2025).
[25] A. R. Subhashri, T. Radhika, Robust dissipativity analysis for stochastic Markov jump competitive neural networks
with mixed delays, Journal of Applied Mathematics and Computing, 71(1) (2025), 801-828. https://doi.org/10.
1007/s12190-024-02257-3
[26] K. Y. Xie, C. K. Zhang, S. Lee, Y. Liu, C. Zhai, Sector bound-dependent matrix-separation-based inequality and its
application to stability analysis of discrete-time delayed genetic regulatory networks, IEEE Transactions on Circuits
and Systems II: Express Briefs, 71(8) (2024), 3785-3789. https://doi.org/10.1109/TCSII.2024.3367777
[27] J. Yan, B. Hu, Z. H. Guan, D. X. Zhang, State bounding for discrete-time switched genetic regulatory networks
with time delay and exogenous disturbances, Neural Networks, 192 (2025), 107910. https://doi.org/10.1016/j.
neunet.2025.107910
[28] J. Yang, J. Jian, Dissipativity analysis of memristive inertial competitive neural networks with mixed delays, Neural
Processing Letters, 56(3) (2024), 151. https://doi.org/10.1007/s11063-024-11610-3
[29] J. Yang, S. Wang, Y. Chen, Z. Li, Pinning control-based reconstructibility analysis and state estimation for
Boolean networks, Journal of Systems Science and Complexity, 38(5) (2025), 1-20. https://doi.org/10.1007/
s11424-025-4270-9
[30] Y. Yang, Y. Yu, C. Xu, C. Zou, Passivity analysis of discrete-time genetic regulatory networks with reactiondiffusion
coupling and delay-dependent stability criteria, Electronic Research Archive, 33(5) (2025), 3111-3134.
https://doi.org/10.3934/era.2025136
[31] Y. L. Zhi, Y. Y. Wu, L. Chen, G. Yang, F. Gao, W. Chen, Stability analysis of discrete-time Markovian jump
neural networks with time-varying delays via a new summation inequality, Asian Journal of Control, 27(6) (2025),
3170-3178. https://doi.org/10.1002/asjc.3626
[32] X. Zhou, J. Han, Y. Li, G. Zhang, Further analysis on fixed/preassigned-time projective synchronization of discontinuous fuzzy delayed inertial neural networks, IEEE Access, 13 (2025), 109294-109307. https://doi.org/10.
1109/ACCESS.2025.3582344
Iranian Journal of Fuzzy Systems
Volume 23, Issue 4
July and August 2026
Pages 35-54

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