Dr. Valentin ​Afraimovich


1990  Doctor of Science in Mathematics and Physics, Nizhny Novgorod State University, Russia.

Areas of Specialization

Dynamical systems, qualitative theory of ordinary differential equations, bifurcation theory, strange attractors, space-time chaos, mathematical models of nonequilibrium media, traveling waves in lattice models, analysis of time-series and snapshots, complexity of orbits and dimension-like characteristics in dynamical systemsValentín-Afraimovich, transitive dynamics in networks of active elements, dynamical networks.

Positions Held

1998-present Professor–researcher, IICO Universidad Autónoma de San Luis Potosí  S.L.P. México. 1996.

Professional Affiliations and Memberships

Member of the Nizhny Novgorod Mathematical Society, Russia.

Awards and Grants

2012 Premio Universitario a la Investigacion Universidad Autonoma de San Luis Potosí, México.

2012 Lagrange Award 2012, IEEE Conference. Nonlinear Science and Complexity.

Service to the Mathematical and Physical Community

Referee of CHAOS. 2006-present. Member of the Advisory Board.

International Journal Of Bifurcation And Chaos In Applied Science And Engineering.

Member of the Editors Board Chaos, Solitons and Fractals. The interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, 2011.

Book Series Editor H.E.P. & L&H Press. Mathematical Methods and Modeling. ISSN 2166-3440. Series Editor, 2012.

Organization of Conferences and Workshops

2015 Chaos, complexity and transport. 1-5 June 2015. Marseilles, France. Scientific Committee.

2014. 5th  International Conference on Nonlinear Science and Complexity. Xi’an jiaotong University, Xi’an, China. August 4-9, 2014. Co-Chair.

Principal Publications Books:

Bifurcation Theory and Catastrophe Theory, with V.I. Arnold, Yu.S.Il'yashenko, L.P. Shil'nikov, Springer-Verlag, 1999.

Lectures in Chaotic Dynamics, with S.-B. Hsu, AMS/IP Studies in Advanced Mathematics, (28), International Press, 2003.

Fractal Dimensions for Poincare Recurrences, with E. Ugalde and J. Urias, Elsevier, 2006.

Long-range Interactions, Stochasticity and Fractional Dynamics, A. Luo, V. Afraimovich editors. HEP- Springer, 2010. ISBN 978-3-642-12342-9

Hamiltonian Chaos Beyond the KAM Theory, A lUo, V. Afraimovich editors. HEP-Springer, 2010. ISBN 978-3-642-12717-5

Fractal Dimensions for Poincare Recurrences, with E. Ugalde and J. Urias.  Russian Translation 2011. ISBN 978-5-93972-903-1

Discrete and Switching Dynamical Systems. A. Luo and V.Afraimovich, eds. Higher Education Press Limited Company, Baijing, China. 2012. ISBN 978-1-62155-002-0 DOI 10.5890/978-1-62155-003-7.

Continuous Dynamical Systems. A. Luo and V. Afraimovich, eds. Education Press Limited Company, Baijing, China. 2012. ISBN 978-1-62155-000-6, DOI 10.5890/978-1-62155-001-3

Nonlinear Dynamics and Complexity (Nonlinear Systems and Complexity). Valentin  Afraimovich, Albert C. J. Luo, Xilin Fu, editors. Springer-Verlag Gmbh. 2014. Nonlinear Systems and Complexity ISBN-10: 3319023527. ISBN-13: 978-3319023526. 1-265 p.

Complex Motions and Chaos in Nonlinear Systems V. Afraimovich, J.A.T. Machado, J. Zhang (Eds.). Springer-Verlag Gmbh. 2016. Series: Nonlinear Systems and Complexity, Vol. 15



1. Stochastic synchronization of oscillations in dissipative systems (with N.N.Verichev and M.I. Rabinovich), Radiofizika, 29 (9), 1050-1060 (1986) (in Russian).

2. On the appearance and structure of the Lorenz attractor (with V.V. Bykov and L.P. Shil'nikov), Soviet Math. Dokl., 234 (1977).

3. Transient Cognitive Dynamics, Metastability, and Decision Making (M. Rabinovich, R. Huerta, P. VArona, V. Afraimovich) PLOS Computational Biology 04, 05: 1-9. 2008.

4. On the origin of reprducible sequential activity in neural circuits (With V. Zhigulin and M. Rabinovich) Chaos 14 (2004), 1123-1129.

5. Chaos of traveling waves in a discrete chain of diffusively coupled maps (with V.I. Nekorkin), International Journal of Bifurcation and Chaos, 4 (3) (1994).

6. Heteroclinic contours in neural ensembles and the winnerless competition principle. (With M. I. Rabinovich, P. Varona) Internat. J. Bifur. Chaos Appl. Sci. Engrg. 14 (2004), no. 4, 1195–1208.

7. Pesins dimension of Poincarè recurrences, Chaos, 7, N1, 1997, 12-20

8. Information flow dynamics in the brain. (Rabinovich MI, Afraimovich VS, Bick C, Varona P.). Phys Life Rev. 2011 Nov 17.

9. Synchronization in lattices of coupled oscillators (with J.K. Hale and S-N. Chow), Physica D, V.103 (1997), 445-451.

10. Fractal and multifractal properties of exit times and Poincare recurrences (with G.M. Zaslavsky), Phys. Rev. E 55, N5 (1997), 5440-5427.

11. Traveling waves in lattice models of multidimensional and multicomponent media. II. Ergodic properties and dimension (with Ya. Pesin and A. Tempelman), Chaos, 3 (1993), 233-241.

12. Pointwise dimensions for Poincaré recurrences associated with maps and special flows (with J. R. Chazottes and B. Saussol), Discrete and Continuous dynamical systems, 9, 2, (2003), pp 263–280.

13. Generation and Reshaping of Sequences in Neural Systems (With M. Rabinovich, R. Huerta and P. Varona) Biological Cybernetics 95:519-536. 2006.

14. Multivalued mappings in generalized chaos synchronization (with N.F.Rulkov, C.T.Lewis, J.- R. Chazottes and A.Cordonet),Phys.Rev.E, vol.64 (2001), 016217.

15. Space time complexity in Hamiltonian dynamics (with G.M. Zaslavsky), Chaos, 13, 2, (2003), pp 519– 532.

16. Symbolic Dynamics in Multidimensional Annulus and Chimera States. V. S. Afraimovich, L. P. Shilnikov. International Journal of Bifurcation and Chaos. Vol: 24, N: 08 (August 2014) DOI: 10.1142/S0218127414400021, 1440002.

17. Hierarchical Heteroclinics in Dynamical Model of Cognitive Processes: Chunking. Valentin S. Afraimovich, Todd R. Young, Mikhail I. Rabinovich. International Journal of Bifurcation and Chaos Vol. 24, No. 10, 1450132 (2014)

18. Sequential Memory: Binding dynamics. V. Afraimovich, X. Gong, M. Rabinovich. CHAOS 25, 103118 (2015).   doi: 10.1063/1.4932563

Scientific  Heritage  of L. P. Shilnikov Valentin S. Afraimovich,  Sergey V. Gonchenko ,LevM.Lerman, Andrey L. Shilnikov, and  Dmitry V. Turaev.  ISSN 1560-3547, Regular and Chaotic Dynamics, 2014, Vol. 19, No. 4, pp. 435–460. Pleiades Publishing, Ltd., 2014.

19. Directional Complexity and entropy for Lift Mappings. V. Afraimovich. M. Courbage, L. Glebsky. Discrete and Continuous Dynamical Systems. Series B. Mathematical Modelling, Analysis and Computations. Volume 20, Number 10. December 2015.

20. Two dimensional heteroclinic attractor in the generalized Lotka-Volterra system. VS Afraimovich, G

Moses, TR Young. Nonlinearity 29 (2016). 1645-1667. doi:10.1088/0951-7715/29/5/1645.

email: valentin@cactus.iico.uaslp.mx