b5ae1c88-4cfe-4296-828f-58710e5addf620240124073025041wseas:wseasmdt@crossref.orgMDT DepositInternational Journal on Applied Physics and Engineering2945-048910.37394/232030https://wseas.com/journals/ape/index.php182024182024310.37394/232030.2024.3https://wseas.com/journals/ape/2024.phpAdelaIonescuDepartment of Applied Mathematics University of Craiova 13 A.I.Cuza Str. Craiova ROMANIAThis paper continues some recent work in a powerful mathematical domain, with applications in connected scientific fields, namely the stability of dynamical systems. In fluid mechanics, stabilizing a dynamical system is a challenging task and it can be done by various ways. Stabilizing a dynamical system could be often easier if we approach controllable systems, because in this form, there can be imposed some bounds on its behavior, by studying the improvement of the operators that describe the system. In this paper, the mixing flows dynamical systems are taken into account, more exactly the kinematics of mixing flows. The stability analysis of the mixing flow is taken into account, in the case of perturbation with a logistic term. The results can be extended to some other versions of the model.1242024124202411162https://wseas.com/journals/ape/2024/a04ape-002(2024).pdf10.37394/232030.2024.3.2https://wseas.com/journals/ape/2024/a04ape-002(2024).pdfJ.M. McDonough, Introductory lectures on turbulence. Physics, Mathematics and Modelling, Univ. of Kentucky, 2007 10.1098/rsta.1895.0004O. Reynolds, On the dynamical theory of turbulent incompressible viscous fluids and the determination of the criterion, Phil. Trans. R. Soc. London A 186, 123–161, 1894 Ionescu, A, Recent Trends in Computational Modeling of Excitable Media Dynamics. Lambert Academic Publishing, 2010 Ottino, J, The Kinematic of Mixing: Stretching, Chaos and Transport. Cambridge Texts in Applied Mathematics. Cambridge University Press, 1989 10.1002/aic.690270406Ottino, J.M., W.E. Ranz, C.W. Macosko. A framework for the mechanical mixing of fluids. AlChE J. 27, pp 565-577. 1981 10.1017/s0025557200073836Krasovskii, N, Stability of Motion. Applications of Lyapunov’s second method to differential systems and equations with delay. Trans. by J. L. Brenner. Stanford University Press, 1963 Isidori, A, Nonlinear Control Systems. Springer Verlag, 1989 10.3934/dcdsb.2015.20.8iGiesl, P, Hafstein,S, Review on computational methods for Lyapunov functions. Discrete and Continuous Dynamical Systems SeriesB, 2015, 20(8), pp1-41 10.1109/tac.2016.2647253Ahmadi, A. A. and Parrilo, P. A, Sum of squares certificates for stability of planar, homogeneous and switched systems. IEEE Transactions on Automatic Control, 2017 62(10), pp 5269–5274 E. Sontag, Mathematical Control Theory. Deterministic Finite Dimensional Systems, 2nd edition, Springer-Verlag New York, 1998 10.3934/dcdsb.2015.20.2361Anderson, J, Papadimitriou, A, Advances in computational Lyapunov analysis using sum-ofsquares programming. Discrete and Continuous Dynamical systems series B, vol 20(8), 2015, pp 2361-2381 Ionescu, A, Stability conditions for the mixing flow dynamical system in a perturbed version. Atti della Accademia Peloritana dei Pericolanti, 2019, 97(2), ppA5-1-A5-10 Ionescu, A., Initial versus Feedback Linearized form for Dynamic Systems. Qualitative approach for models arising from excitable media. Advances in Mathematics Research, Nova Science Publishers New York 2020, pp 1-41 10.5772/intechopen.96872Ionescu, A., Qualitative analysis for controllable dynamical systems. Stability with control Lyapunov functions. Advances in dynamical systems theory. Models, algorithms and applications, InTech Open Novisad 2021, pp 1-14