This image shows Viktor Avrutin

Viktor Avrutin

Prof. Dr.

Institute for Systems Theory and Automatic Control

Contact

+49 711 685 67103
+49 711 685 57103

Pfaffenwaldring 9
70569 Stuttgart
Germany
Room: 3.236

Subject

I'm working on the field of nonlinear dynamics. I'm mainly interested in bifurcation theory, particularly for piecewise smooth sytems, in border collision and homoclinic bifurcations, in low-dimensional chaos and bifurcations of chaotic attractors (crises). My further research interests include numerics, simulation software and algorithms, as well as neural networks.

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Scopus Author ID: 6603800718

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https://doi.org/10.1142/8285

  1. (Journal-) Articles

    1. Avrutin, V., Panchuk, A., & Sushko, I. (2023). Can a border collision bifurcation of a chaotic attractor lead to its expansion? Proc. R. Soc. A, 479(2277), Article 2277. https://doi.org/10.1098/rspa.2023.0260
    2. Zhusubaliyev, Zh. T., Avrutin, V., Kucherov, A., Haroun, R., & Aroudi, A. E. (2023). Period adding with symmetry breaking/recovering in a power inverter with hysteresis control. Physica D, 444, 133600. https://doi.org/10.1016/j.physd.2022.133600
    3. Avrutin, V., Dal~Forno, A., & Merlone, U. (2023). Codimension-2 Bifurcations in a Quantum Decision Making Model. Int. J. Bif. Chaos, 33(13), Article 13. https://doi.org/10.1142/S021812742330032X
    4. Jeffrey, M., & Avrutin, V. (2022). Periods 1 + 2 imply chaos in steep or nonsmooth maps. Nonlinearity, 35, 6014–6041. https://doi.org/10.1088/1361-6544/ac9506
    5. Zhusubaliyev, Zh. T., Avrutin, V., Sushko, I., & Gardini, L. (2022). Border Collision Bifurcation of a Resonant Closed Invariant Curve. Chaos, 32, 043101. https://doi.org/10.1063/5.0086419
    6. Avrutin, V., von Schwerin-Blume, L., Zhusubaliyev, Zh. T., Haroun, R., & Aroudi, A. E. (2022). Noise-induced and border-collision-induced bubbling. Physica D, 435, 133277. https://doi.org/10.1016/j.physd.2022.133277
    7. Kryzhevich, S., Avrutin, V., & Söderbacka, G. (2022). Bistability in a One-Dimensional Model of a Two-Predators-One-Prey Population Dynamics System. Lobachevskii Journal of Mathematics, 43(2), Article 2. https://arxiv.org/abs/2108.06739
    8. Zhusubaliyev, Zh. T., Avrutin, V., Rubanov, V. G., & Bushuev, D. A. (2021). Complex dynamics of a vibration machine caused by a relay feedback control. Physica D, 420, 132870. https://doi.org/10.1016/j.physd.2021.132870
    9. Avrutin, V., Zhusubaliyev, Zh. T., & Bastian, F. (2021). Transformations of Closed Invariant Curves and Closed-Invariant-Curve-Like Chaotic Attractors in Piecewise Smooth Systems. Int. J. Bifurcat. Chaos, 31(3), Article 3. https://doi.org/10.1142/S0218127421300093
    10. Jeffrey, M. R., & Avrutin, V. (2021). Bifurcations of hidden orbits in discontinuous maps. Nonlinearity, 34(9), Article 9. https://doi.org/10.1088/1361-6544/ac12ac
    11. Avrutin, V., Panchuk, A., & Sushko, I. (2021). Border collision bifurcations of chaotic attractors in one-dimensional maps with multiple discontinuities. Proc. R. Soc. A, 477, 20210432. https://doi.org/10.1098/rspa.2021.0432
    12. Zhusubaliyev, Zh. T., Avrutin, V., & Medvedev, A. (2021). Doubling of a closed invariant curve in an impulsive Goodwin’s oscillator with delay. Chaos, Solitons & Fractals, 153(1), Article 1. https://doi.org/10.1016/j.chaos.2021.111571
    13. Avrutin, V., Zhusubaliyev, \zh.T., & Aroudi, A. E. (2021). Non-visible Transformations of Chaotic Attractors due to their Ultra Low Density in AC-DC Power Factor Correction Converters. Nonlinear Dynamics, 102, 2905–2924. https://doi.org/10.1007/s11071-020-06077-5
    14. Avrutin, V., Bastian, F., & Zhusubaliyev, Zh. T. (2021). A geometric approach to bubbling. Physica D, 417, 132808. https://doi.org/10.1016/j.physd.2020.132808
    15. Kryzhevich, S., Avrutin, V., Begun, N., Rachinskii, D., & Tajbakhs, K. (2021). Dynamics of Systems with a Discontinuous Hysteresis Operator and Interval Translation Maps. Axioms (Special Issue ``Topological Theory of Dynamical Systems’’), 10(2), Article 2. https://doi.org/10.3390/axioms10020080
    16. Sushko, I., Avrutin, V., & Gardini, L. (2021). Center Bifurcation in the Lozi Map. Int. J. Bifurcat. Chaos, 31(16), Article 16. https://doi.org/10.1142/S0218127421300469
    17. Avrutin, V., & Zhusubaliyev, Zh. T. (2020). Piecewise-linear map for studying border-collision phenomena in DC/AC converters. Int. J. Bifurcat. Chaos, 30(7), Article 7. https://doi.org/10.1142/S0218127420300153
    18. Simpson, D., Avrutin, V., & Banerjee, S. (2020). Nordmark map and the problem of large-amplitude chaos in impact oscillators. Phys. Rev. E, 102(2), Article 2. https://doi.org/10.1103/PhysRevE.102.022211
    19. Avrutin, V., Zh.T., Z., Suissa, D., & A., E. A. (2020). Non-observable chaos in piecewise smooth systems. Nonlinear Dynamics, 99(3), Article 3. https://doi.org/10.1007/s11071-019-05406-7
    20. Avrutin, V., Zhusubaliyev, Zh. T., Suissa, D., & Aroudi, A. E. (2020). Non-observable chaos in piecewise smooth systems. Nonlinear Dynamics, 99(3), Article 3. https://doi.org/10.1007/s11071-019-05406-7
    21. Avrutin, V., Zhusubaliyev, Zh. T., & El Aroudi, A. (2020). Non-visible Transformations of Chaotic Attractors due to their Ultra Low Density in AC-DC Power Factor Correction Converters. Nonlinear Dynamics, 102, 2905–2924. https://doi.org/10.1007/s11071-020-06077-5
    22. Avrutin, V., & Zhusubaliyev, Zh. T. (2019). Nested closed invariant curves. Int. J. Bifurcat. Chaos, 29(7), Article 7. https://doi.org/10.1142/S0218127419300179
    23. Medvedev, A., Mattsson, P., Zhusubaliyev, Zh. T., & Avrutin, V. (2018). Nonlinear dynamics and entrainment in a continuously forced pulse-modulated model of testosterone regulation. Nonlinear Dynamics, 94(2), Article 2. https://doi.org/10.1007/s11071-018-4416-6
    24. Zhusubaliyev, Zh. T., Avrutin, V., Rubanov, V., Bushuev, D., Titov, D., & Yanochkina, O. (2018). Persistence Border Collisions in a Vibrating System Excited by an Unbalanced Motor with a Relay Control. AIP Conf. Proc., 1959, 080022. https://doi.org/10.1063/1.5034739
    25. Avrutin, V., Zhusubaliyev, Zh. T., & Mosekilde, E. (2017). Cascades of alternating pitchfork and flip bifurcations in H-bridge inverters. Physica D, 345, 27–39. https://doi.org/10.1016/j.physd.2016.12.008
    26. Panchuk, A., Sushko, I., & Avrutin, V. (2017). Bifurcation Structures in a Bimodal Piecewise Linear Map. Front. Appl. Math. Stat., 3(7), Article 7. https://doi.org/10.3389/fams.2017.00007
    27. Avrutin, V., Morcillo, J. D., Zhusubaliyev, Zh. T., & Angulo, F. (2017). Bubbling in a power electronic inverter: Onset, development and detection. Chaos, Solitons & Fractals, 104, 135–152. https://doi.org/10.1016/j.chaos.2017.08.003
    28. Avrutin, V., Zhusubaliyev, Zh. T., Saha, A., Banerjee, S., Gardini, L., & Sushko, I. (2017). Dangerous Bifurcations Revisited. Int. J. Bifurcat. Chaos, 26(14), Article 14. https://doi.org/10.1142/S0218127416300408
    29. Avrutin, V., Zhusubaliyev, Zh. T., El Aroudi, A., Fournier-Prunaret, D., Garcia, G., & Mosekilde, E. (2016). Disrupted bandcount doubling in an AC-DC boost PFC circuit modeled by a time varying map. J. of Physics, 692(1), Article 1. https://doi.org/10.1088/1742-6596/692/1/012003
    30. Belopolskaya, M., Avrutin, V., Firsov, S., & Yakovlev, A. (2016). Potential Applications of Serum HBsAg Level Measurement in  Patients with Hepatitis B and D Co-Infection. Gastroenterology & Hepatology, 5(7), Article 7. https://doi.org/10.15406/ghoa.2016.05.00170
    31. Avrutin, V., Zhusubaliyev, Zh. T., & Mosekilde, E. (2016). Border collisions inside the stability domain of a fixed point. Physica~D, 321–322, 1–15. https://doi.org/10.1016/j.physd.2016.02.011
    32. Sushko, I., Gardini, L., & Avrutin, V. (2016). Nonsmooth One-dimensional Maps: Some Basic Concepts and Definitions. J. Differ. Equations Appl., 22(12), Article 12. https://doi.org/10.1080/10236198.2016.1248426
    33. Belopolskaya, M., Avrutin, V., Firsov, S., & Yakovlev, A. (2015). HBsAg level and Hepatitis B viral load correlation with focus on pregnancy. Annals of Gastroenterology, 28(3), Article 3.
    34. Panchuk, A., Sushko, I., & Avrutin, V. (2015). Bifurcation structures in a bimodal piecewise linear map: chaotic dynamics. Int. J. Bifurcat. Chaos, 25(3), Article 3. https://doi.org/10.1142/S0218127415300062
    35. Tramontana, F., Sushko, I., & Avrutin, V. (2015). Period adding structure in a 2D discontinuous model of economic growth. Applied Mathematics and Computation, 253, 262–273.
    36. Sushko, I., Tramontana, F., Westerhoff, F., & Avrutin, V. (2015). Symmetry breaking in a bull and bear financial market model. Chaos, Solinons & Fractals, 79, 57–72.
    37. Sushko, I., Avrutin, V., & Gardini, L. (2015). Bifurcation structure in the skew tent map and its application as a border collision normal form. J. of Diff. Equations and Applications, 1–48.
    38. Avrutin, V., Clüver, M., Mahout, V., & Fournier-Prunaret, D. (2015). Bandcount adding structure and collapse of chaotic attractors in a piecewise linear bimodal map. Physica D, 309, 37–56.
    39. Avrutin, V., Mosekilde, E., Zhusubaliyev, Zh. T., & Gardini, L. (2015). Onset of chaos in a single-phase power electronic inverter. Chaos, 25, 043114.
    40. Avrutin, V., Dibak, Ch., Dal Forno, A., & Merlone, U. (2015). Dynamics of a 2D piecewise linear Braess paradox model: Effect of the third partition. Int. J. Bifurcat. Chaos, 25(11), Article 11.
    41. Avrutin, V., Schenke, B., & Gardini, L. (2015). Calculation of homoclinic and heteroclinic orbits in 1D maps. Communications in Nonlinear Science and Numerical Simulation, 22(1–3), Article 1–3.
    42. Avrutin, V., Gardini, L., Schanz, M., & Sushko, I. (2014). Bifurcations of chaotic attractors in one-dimensional piecewise smooth maps. Int. J. Bifurcat. Chaos, 24(8), Article 8.
    43. Radi, D., Gardini, L., & Avrutin, V. (2014). The Role of Constraints in a Segregation Model: The Asymmetric Case. Discrete Dynamics in Nature and Society, 2014, Article ID 569296, 17 pages.
    44. Avrutin, V., Sushko, I., & Tramontana, F. (2014). Bifurcation structure in a bimodal piecewise linear business cycle model. Abstract and Applied Analysis, 2014, Article ID 401319, 12 pages.
    45. Avrutin, V., Sushko, I., & Gardini, L. (2014). Cyclicity of chaotic attractors in one-dimensional discontinuous maps. Mathematics and Computers in Simulation (Special Issue ``Discontinuous Dynamical Systems: Theory and Numerical Methods’’), 95, 126–136. https://doi.org/10.1016/j.matcom.2012.07.019
    46. Radi, D., Gardini, L., & Avrutin, V. (2014). The Role of Constraints in a Segregation Model: The Symmetric Case. Chaos, Solitons & Fractals, 66, 103–119.
    47. Dal Forno, A., Merlone, U., & Avrutin, V. (2014). Dynamics in Braess paradox with non-impulsive commuters. Discrete Dynamics in Nature and Society, 2014, 345795.
    48. Gardini, L., Avrutin, V., & Sushko, I. (2014). Codimension-2 border collision bifurcations in one-dimensional discontinuous piecewise smooth maps. Int. J. Bifurcat. Chaos, 24(2), Article 2.
    49. Avrutin, V., Eckstein, B., Schanz, M., & Schenke, B. (2014). Bandcount incrementing scenario revisited and floating regions within robust chaos. Mathematics and Computers in Simulation (Special Issue ``Discontinuous Dynamical Systems: Theory and Numerical Methods’’), 95, 23–38. https://doi.org/10.1016/j.matcom.2013.06.001
  2. Monograhs

    1. Avrutin, V., Gardini, L., Sushko, I., & Tramontana, F. (2019). Continuous and Discontinuous Piecewise-Smooth One-dimensional Maps: Invariant Sets and Bifurcation Structures. In Nonlinear Science, Series~A (Vol. 95). World Scientific. https://doi.org/10.1142/8285
  3. Contributions to anthologies

    1. Avrutin, V., Gardini, L., Sushko, I., Zhusubaliyev, Zh. T., & Sopuev, U. (2023). Border Collision and Heteroclinic Bifurcations in a 2D Piecewise Smooth Map. In S. Elaydi, M. Kulenović, & S. Kalabusić (Eds.), Advances in Discrete Dynamical Systems, Difference Equations and Applications (pp. 61–73). Springer. https://doi.org/10.1007/978-3-031-25225-9_3
  4. Conference papers

    1. Simpson, D., Avrutin, V., & Banerjee, S. (2019). Nordmark map and the problem of large-amplitude chaos in an impact oscillator. Proc. 15th Int. Conf. Dynamical Systems - Theory and Applications.
    2. Belopolskaya, M., Avrutin, V., Dmitriev, A., & Yakovlev, A. (2019). Effects of direct acting antiviral drugs on a fibrosis in patients with cirrhotic stage of hepatitis C. Rev. in Antiviral Therapy & Infectious Deseases (Proc. 5th Central and Eastern European Meeting on Viral Hepatitis and HIV).
    3. Avrutin, V., Zhusubaliyev, Zh. T., & Aroudi, A. E. (2018). Non-Observable Chaos in Power Converters. Proc. of Int. Symp. on Nonlinear                  Theory and Its Applications (NOLTA2018).
    4. Zhusubaliyev, Zh. T., Avrutin, V., Rubanov, V., Bushuev, D., Titov, D., & Yanochkina, O. (2018). Persistence border collisions in a vibration system with a relay control. Proc. Int. Symp. on Nonlinear Theory and Its Applications (NOLTA).
    5. Avrutin, V., Zhusubaliyev, Zh. T., & Mosekilde, E. (2017). Low-dimensional piecewise smooth maps with an unpredictable number of switching manifolds. Proc. 9th European Nonlinear Dynamics Conference (ENOC).

2020: Appointment as an extraordinary professor (Apl. Prof.) at the University of Stuttgart, Germany.

2011: Status of Privatdozent (PD) and venia docendi from the University of Stuttgart, Germany.

2010: Habilitation in Computer Science and the degree Dr. rer. nat. habil. from the University of Stuttgart, Germany.
Title of the Habilitation thesis “Bifurcation structures within robust chaos: computational aspects, numerical investigation and analytic explanation”.

2003: Ph.D. degree from the University of Stuttgart, Germany. Title of the Ph.D. thesis “Zum Verhalten dynamischer Systeme mit einer stückweise-glatten Systemfunktion” (English: “Some aspects of the behavior of piecewise-smooth dynamical systems”).

1997: M.Sc. degree in Computer Science with Mathematics from the University of Stuttgart, Germany.

1992: B.Sc. degree from the St. Petersburg State Polytechnical University, Russia.

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