Stability analysis of the stochastic Grey-Scott model using spectral method
Corresponding Author
Sami Ullah Khan
Department of Mathematics, City University of Science and Information Technology Peshawar, Peshawar, Pakistan
Correspondence
Sami Ullah Khan, Department of Mathematics, City University of Science and Information Technology Peshawar, Peshawar, KP, 2500, Pakistan.
Email: [email protected]
Communicated by: T. E. Simos
Contribution: Conceptualization, Writing - original draft, Methodology, Software, Supervision
Search for more papers by this authorMohamed Altanji
Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
Contribution: Investigation, Formal analysis
Search for more papers by this authorHassan A. Jari
Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia
Contribution: Data curation, Validation, Visualization
Search for more papers by this authorAbdullah A. Faqihi
Department of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia
Contribution: Investigation, Visualization, Formal analysis, Software
Search for more papers by this authorCorresponding Author
Sami Ullah Khan
Department of Mathematics, City University of Science and Information Technology Peshawar, Peshawar, Pakistan
Correspondence
Sami Ullah Khan, Department of Mathematics, City University of Science and Information Technology Peshawar, Peshawar, KP, 2500, Pakistan.
Email: [email protected]
Communicated by: T. E. Simos
Contribution: Conceptualization, Writing - original draft, Methodology, Software, Supervision
Search for more papers by this authorMohamed Altanji
Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia
Contribution: Investigation, Formal analysis
Search for more papers by this authorHassan A. Jari
Department of Computer Science, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia
Contribution: Data curation, Validation, Visualization
Search for more papers by this authorAbdullah A. Faqihi
Department of Industrial Engineering, College of Engineering and Computer Science, Jazan University, Jazan, Saudi Arabia
Contribution: Investigation, Visualization, Formal analysis, Software
Search for more papers by this authorAbstract
The Grey-Scott model is a prominent reaction–diffusion system that has sustain consequential recent research about patterning creation in the reaction–diffusion systems. The present research work, explore the stability analysis of a proposed stochastic Grey-Scott model, which recommend the randomness or unpredictability into the complex system. To take into account the different variations in reactant concentrations profiles, the stochasticity is modeled using the additive white noise terms. To investigate the stability characteristics of the stochastic Grey-Scott model, we use the spectral collocation technique. Such mathematical perspective sheds light on the different system's behavior in the addition of white noise, and also it may have significance for comprehending processes in the real world that are controlled by comparable dynamics.
CONFLICT OF INTEREST STATEMENT
The authors declare no conflict of interest.
REFERENCES
- 1D. Tholens, Travelling waves in stochastic reaction-diffusion equations, 2018.
- 2T. V. Olde Scheper, Controlled bio-inspired self-organised criticality, PloS ONE 17 (2022), no. 1, e0260016.
- 3A. Stokes. (2020). Network analysis of simulated and real indigenous irrigation system, Doctoral dissertation, University of Southampton).
- 4D. Karig, K. M. Martini, T. Lu, N. A. DeLateur, N. Goldenfeld, and R. Weiss, Stochastic Turing patterns in a synthetic bacterial population, Proc. Natl. Acad. Sci. 115 (2018), no. 26, 6577.
- 5U. Deichmann, Self-organization and genomic causality in models of morphogenesis, Entropy 25 (2023), no. 6, 873.
- 6M. Grace and M. T. Hütt, Regulation of spatiotemporal patterns by biological variability: general principles and applications to Dictyostelium discoideum, PLoS Comput. Biol. 11 (2015), no. 11, e1004367.
- 7D. Pathak, P. Agrawal, A. A. Efros, and T Darrell, Curiosity-driven exploration by self-supervised prediction, In International Conference on Machine Learning. PMLR, 2017, pp. 2778–2787.
- 8Z. Wang, M. A. Andrews, Z. X. Wu, L. Wang, and C. T. Bauch, Coupled disease–behavior dynamics on complex networks: a review, Phys. Life Rev. 15 (2015), 1–29.
- 9C. E. Finch and T. B. Kirkwood, Chance, development and aging, Oxford University Press, USA, 2000.
- 10P. E. Purnick and R. Weiss, The second wave of synthetic biology: from modules to systems, Nature Rev. Mol. Cell Biol. 10 (2009), no. 6, 410–422.
- 11M. Grieves and J. Vickers, Digital twin: Mitigating unpredictable, undesirable emergent behavior in complex systems, 2017. Transdisciplinary perspectives on complex systems: New findings and approaches, 85–113.
- 12M. Cruz and R. Beckett, Bioreceptive design: a novel approach to biodigital materiality, Arq: Archit. Res. Quart. 20 (2016), no. 1, 51–64.
- 13A. Stokes. (2020). Network analysis of simulated and real indigenous irrigation system, Doctoral dissertation, University of Southampton).
- 14S. U. Khan and I. Ali, Numerical analysis of stochastic SIR model by Legendre spectral collocation method, Advances in Mechanical Engineering, SAGE Publications Sage UK: London, England, Vol. 11, 2019, pp. 7.
- 15S. U. Khan and I Ali, Applications of Legendre spectral collocation method for solving system of time delay differential equations, Adv. Mech. Eng. 12 (2020), no. 6, 1687814020922113.
- 16S. U. Khan and I. Ali, Convergence and error analysis of a spectral collocation method for solving system of nonlinear Fredholm integral equations of second kind, Comput. Appl. Math. 38 (2019), no. 3, 125.
- 17I. Ali and S. U. Khan, Analysis of stochastic delayed SIRS model with exponential birth and saturated incidence rate, Chaos, Solitons Fract. 138 (2020), 110008.
- 18E. A. Algehyne, F. U. Khan, S. U. Khan, W. Jamshed, and E. S. M. Tag El Din, Dynamics of stochastic Zika virus with treatment class in human population via spectral method, Symmetry 14 (2022), no. 10, 2137.
- 19I. Ali and S. U. Khan, A dynamic competition analysis of stochastic fractional differential equation arising in finance via pseudospectral method, Mathematics 11 (2023), no. 6, 1328.
- 20N. Gul, Transmission dynamic of stochastic hepatitis C model by spectral collocation method, Comput. Methods Biomech. Biomed. Engin. 25 (2022), no. 5, 578–592.
- 21T. C. Meng, S. Somani, and P. Dhar, Modeling and simulation of biological systems with stochasticity, In Silico Biol. 4 (2004), no. 3, 293–309.
- 22B. Bravi and G Longo, The unconventionality of nature: biology, from noise to functional randomness, In Unconventional Computation and Natural Computation: 14th International Conference, UCNC 2015, Auckland, New Zealand, August 30–September 3, 2015, Proceedings 14 (pp. 3–34). Springer International Publishing, 2015.
10.1007/978-3-319-21819-9_1 Google Scholar
- 23P. M. Riechers and J. P. Crutchfield, Fraudulent white noise: flat power spectra belie arbitrarily complex processes, Phys. Rev. Res. 3 (2021), no. 1, 013170.
- 24M. Z. Lubis and M. Si, Signal processing for power spectral density (PSD), 2016. Signal processing for marine acoustic and dolphin using matlab, Edition.
- 25T. Keenan, J. Maria Serra, F. Lloret, M. Ninyerola, and S. Sabate, Predicting the future of forests in the Mediterranean under climate change, with niche-and process-based models: CO2 matters!, Global Change Biol. 17 (2011), no. 1, 565–579.
- 26F. Giampaolo, M. De Rosa, P. Qi, S. Izzo, and S. Cuomo, Physics-informed neural networks approach for 1D and 2D Gray-Scott systems, Adv. Modeling Simul. Eng. Sci. 9 (2022), no. 1, 1–17.
- 27A. Fofonjka and M. C. Milinkovitch, Reaction-diffusion in a growing 3D domain of skin scales generates a discrete cellular automaton, Nat. Commun. 12 (2021), no. 1, 2433.
- 28S. T. Vittadello and M. P. Stumpf, Open problems in mathematical biology, Math. Biosci. 354 (2022), no. 108926.
- 29A. Ali, On dynamics of stochastic avian influenza model with asymptomatic carrier using spectral method, 2022. Mathematical Methods in the Applied Sciences.
- 30A. Azizi, H. Mobki, H. M. Ouakad, and O. R. B. Speily, Applied mechatronics: on mitigating disturbance effects in MEMS resonators using robust nonsingular terminal sliding mode controllers, Machines 10 (2022), no. 1, 34.
- 31A. Azizi, M. Naderi Soorki, T. Vedadi Moghaddam, and A. Soleimanizadeh, A new fractional-order adaptive sliding-mode approach for fast finite-time control of human knee joint orthosis with unknown dynamic, Mathematics 11 (2023), no. 21, 4511.
- 32H. Mobki, A. M. Sabegh, A. Azizi, and H. M. Ouakad, On the implementation of adaptive sliding mode robust controller in the stabilization of electrically actuated micro-tunable capacitor, Microsyst. Technol. 26 (2020), 3903–3916.
- 33A. Azizi and H. Mobki, Applied mechatronics: designing a sliding mode controller for active suspension system, Complexity 2021 (2021), 1–23.
- 34A. Azizi, A case study on designing a sliding mode controller to stabilize the stochastic effect of noise on mechanical structures: residential buildings equipped with ATMD, Complexity 2020 (2020), 1–17.
- 35A. Azizi, Computer-based analysis of the stochastic stability of mechanical structures driven by white and colored noise, Sustainability 10 (2018), no. 10, 3419.
- 36A. Azizi, A case study on computer-based analysis of the stochastic stability of mechanical structures driven by white and colored noise: utilizing artificial intelligence techniques to design an effective active suspension system, Complexity 2020 (2020), 1–8.
- 37H. Mobki, M. Jalilirad, M. Vatankhah Moradi, and A. Azizi, Multi input versus single input sliding mode for closed-loop control of capacitive micro structures, SN Appl. Sci. 1 (2019), 1–13.
- 38M. Latifinavid and A. Azizi, Kinematic modelling and position control of a 3-DOF parallel stabilizing robot manipulator, J. Intell. Robot. Syst. 107 (2023), no. 2, 17.
