Lipschitz stability analysis of fractional-order gene regulatory networks with impulsive perturbations and distributed delays

Ivanka Stamova; Cvetelina Spirova; Gani Stamov; Ivanka Stamova; Cvetelina Spirova; Gani Stamov

doi:10.3934/mmc.2025030

Mathematical Modelling and Control

2025, Volume 5, Issue 4: 421-431. doi: 10.3934/mmc.2025030

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Research article

Lipschitz stability analysis of fractional-order gene regulatory networks with impulsive perturbations and distributed delays

1.
Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA
2.
Department of Mathematics, Technical University of Sofia, Sliven 8800, Bulgaria

Received: 26 September 2025 Revised: 18 October 2025 Accepted: 20 October 2025 Published: 08 December 2025

A model of fractional-order discontinuous impulsive delayed gene regulatory networks (GRNs) was investigated in this paper. The impulsive perturbations were at fixed moments of time and measured the impulsive control effects which can be controlled appropriately. A fractional-order modeling approach was applied and distributed delays were taken into account for greater model flexibility. In this paper, rather than studying the classical Lyapunov-type stability of an equilibrium point, we addressed the extended Lipschitz stability behavior of the considered GRNs. By applying the impulsive fractional Lyapunov functions technique, new criteria were derived to ensure the global uniform Lipschitz stability for the fractional impulsive delayed GRNs. Furthermore, the effects of considering uncertain parameters were also analyzed. Finally, an illustrating example was given to support the obtained theoretical results.
- gene regulatory networks,
- impulses,
- distributed delays,
- fractional order,
- Lipschitz stability
Citation: Ivanka Stamova, Cvetelina Spirova, Gani Stamov. Lipschitz stability analysis of fractional-order gene regulatory networks with impulsive perturbations and distributed delays[J]. Mathematical Modelling and Control, 2025, 5(4): 421-431. doi: 10.3934/mmc.2025030

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Abstract

A model of fractional-order discontinuous impulsive delayed gene regulatory networks (GRNs) was investigated in this paper. The impulsive perturbations were at fixed moments of time and measured the impulsive control effects which can be controlled appropriately. A fractional-order modeling approach was applied and distributed delays were taken into account for greater model flexibility. In this paper, rather than studying the classical Lyapunov-type stability of an equilibrium point, we addressed the extended Lipschitz stability behavior of the considered GRNs. By applying the impulsive fractional Lyapunov functions technique, new criteria were derived to ensure the global uniform Lipschitz stability for the fractional impulsive delayed GRNs. Furthermore, the effects of considering uncertain parameters were also analyzed. Finally, an illustrating example was given to support the obtained theoretical results.

References

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