wseas-12071-20260921113252-013653 20260921113252310 wseas/wseas wseas.group@gmail.com WSEAS WSEAS Transactions on Circuits and Systems 1109-2734 2224-266X 03 30 2026 03 30 2026 25 Felix Sadyrbaev Institute of Mathematics and Computer Science University of Latvia Rainis boulevard 29, Riga, LV-1459 LATVIA Valentin Sengileyev Daugavpils University Parades street 1, Daugavpils, LV-5401 LATVIA A review of samples of oscillations in a system of ordinary differential equations that arise in mathematical models of complex networks is provided. Starting from the low-dimensional systems, we go up in the sense of system dimensionality, commenting on various patterns that appear. We overlook examples of relatively large systems (with dimensionality up to 13 equations) that describe leukemia treatment and cellular aging. Visualizations and examples are supplied. The methods used are of geometrical and computational nature, revealing phase space structures and specifics. 09 21 2026 09 21 2026 316 28 https://creativecommons.org/licenses/by/4.0/ 10.37394/23201.2026.25.28 https://wseas.com/journals/articles.php?id=12071 H.R. Wilson, J.D. Cowan. Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons. Biophysical Journal, Volume 12, Issue 1, 1972, Pages 1-24, https://doi.org/10.1016/S0006-3495(72)86068-5 H.R. Wilson, H.R., J.D. Cowan. A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13 (1973), 55–80, https://doi.org/10.1007/BF00288786 Le-Zhi Wang, Ri-Qi Su, Zi-Gang Huang, Xiao Wang, Wen-Xu Wang, Celso Grebogi and Ying-Cheng Lai. A geometrical approach to control and controllability of nonlinear dynamical networks. Nature Communications, Volume 7 (2016), Article number: 11323, https://doi.org/10.1038/ncomms11323 S.P. Cornelius, W.L. Kath and A.E. Motter. Realistic control of network dynamics. Nat. Commun 4(2013), article number: 1942, https://doi.org/10.1038/ncomms2939 K.H. Chong, X. Zhang, J. Zheng. Dynamical analysis of cellular ageing by modeling of gene regulatory network based attractor landscape. PLoS ONE 13(6): e0197838, 2018. https://doi.org/10.1371/journal.pone.0197838 G.H. Waddington. The strategy of the genes: a discussion of some aspects of theoretical biology. ISBN: 9781315765471, London: Allen & Unwin; 1957, https://doi.org/10.4324/9781315765471 I. Belgacem. Logistic Gene Regulatory Networks: A Modelling Framework Beyond Hill Functions. arXiv:2606.11028 (2026). https://arxiv.org/abs/2606.11028 E. Brokan, F. Sadyrbaev. Attraction in n-dimensional differential systems from network regulation theory. Math. Methods Appl. Sci. 2018, 41, 7498–7509. https://doi.org/10.1002/mma.5086 H. Kim, H. Choi, D. Lee, J. Kim. A review on gene regulatory network reconstruction algorithms based on single cell RNA sequencing. Gene Genom. 2024, 46, 1–11. https://doi.org/10.1007/s13258-023-01473-8 M. Marku, V. Pancaldi. From time-series transcriptomics to gene regulatory networks: A review of inference methods. PLoS Comput. Biol. 2023, 19, e1011254. https://doi.org/10.1371/journal.pcbi.1011254 S.I.M. Ali, S.Z. Alrashid. A review of methods for gene regulatory networks reconstruction and analysis. Artif Intell Rev 58, 256 (2025). https://doi.org/10.1007/s10462-025-11257-z