I am interested in applying mathematical methods developed in the field of nonlinear dynamics to other areas of science, like astrophysics, seismology, signal processing, bioinformatics, etc. This activity also includes studying simple mathematical models, such as, for example, Duffing oscillator or mathematical pendulum that are capable of producing complex behavior due to their nonlinearity (harmonics and subharmonics, hysteresis and jumps in the phase space, multistability, bifurcations, chaos, etc.) and, therefore, can be used for modeling complicated phenomena that occur in real life.
Since ancient times, mathematics has been considered as a part of human cultural heritage. As such, it is close to other arts, like painting, or music, or literature, or even theatre. Perhaps, when mathematicians solve complex mathematical problems, they experience feelings similar to composers writing music masterpieces or artists painting pictures. On one hand, it looks very difficult, but on the other, brings a lot of satisfaction in the case of success. However, the satisfaction felt at the momend of creation is more of esthetic value than of practical importance, because it takes sometimes a very long time for a painting to become recognized as an outstanding masterpiece, as well as for a mathematical theory to find its important applications.
Nowadays, the proofs of importance of mathematics can be found everywhere. It is fascinating how mathematical ideas can penetrate our everyday life through various systems and devices, like banking, insurance and finances, cell phones, computers, TV-sets, and other electronic gadgets. Although the significance of mathematics is now commonly accepted by everybody, I believe it is still a science that has an inner beauty to attract people from esthetic viewpoints.
- In nonlinear dynamics: study of mathematical formulas predicting the appearance of chaos in simple physical models like Duffing or Pendulum oscillators under external excitation; application of methods named after Lyapunov and Melnikov.
- In radio astronomy: study of complex radio signals (known as S-bursts) from the planet Jupiter, development of observational equipment and data analysis methods; search for radio signals from distant planets
- In seismology: study of stick-slip models of dry friction as possible mechanism for earthquakes
- In bioinformatics: study of gene expression rates from the viewpoint of random signals theory
In molecular dynamics: aplication of the theory of entropy, complexity, and symbolic dynamics to the analysis of molecular ensembles in water and water-protein systems
- 1. V. B. Ryabov, P. Zarka, S. Hess, A. Konovalenko, G. Litvinenko, V. Zakharenko, V. Shevchenko, B. Cecconi (2014), Fast and slow frequency-drifting millisecond bursts in Jovian decametric radio emissions, Astronomy & Astrophysics, 568, A53 (1-11)
- J.C. Nacher and V.B. Ryabov (2012), Nonlinear response of gene expression to chemical perturbations: a noise-detector model and its predictions, Biosystems, Vol. 107, 9-17.
- V. Ryabov and D. Nerukh (2011), Computational mechanics of molecular systems: quantifying high dimensional dynamics by distribution of Poincare recurrence times, Chaos 21, 037113 (1-9)
- V. Ryabov and D. Nerukh (2011), Quantifying long time memory in phase space trajectories of molecular liquids, J. Mol. Liq., 159 (1), 99-104.
- V. Ryabov (2011), Predicting chaos with second method of Lyapunov, in ” Chaos Theory: Modeling, Simulation and Applications”, Edited by C. H. Skiadas, I. Dimotikalis and C. Skiadas, World Scientific, pp. 341-348.
- V. Ryabov, D. Vavriv, P. Zarka, B. Ryabov, R. Kozhin, V. Vinogradov, L. Denis (2010), A low-noise, high dynamic range digital receiver for radio astronomy applications: An efficient solution for observing radio-bursts from Jupiter, the Sun, Pulsars, and other astrophysical plasmas below 30 MHz, Astronomy & Astrophysics, 510, A16 (1-13)
- Ryabov, V. B., B. P. Ryabov, D. M. Vavriv, P. Zarka, R. Kozhin, V. V. Vinogradov, and V. A. Shevchenko (2007), Jupiter S-bursts: Narrow-band origin of microsecond subpulses, J. Geophys. Res., 112, A09206, doi:10.1029/2007JA012607 (1-20).
- V.B. Ryabov, P. Zarka, and B.P. Ryabov (2004), Search of exoplanetary radio signals in the presence of strong interference: Enhancing sensitivity by data accumulation. Planetary and Space Science, Vol.52, 1479-1491.
- V. B. Ryabov (2002), Using Lyapunov Exponents to Predict the Onset of Chaos in Nonlinear Oscillators, Phys. Rev. E, V. 66, 016214 (1–17).
- V. B. Ryabov, K. Ito (2001), Intermittent Phase Transitions in a Slider-Block Model as a Mechanism for Earthquakes, Pure and Applied Geophysics, V. 158, No.5-6, p.919-930.
- V.B. Ryabov, A.V. Stepanov, P.V. Usik, D.M. Vavriv, V.V. Vinogradov, Yu. A. Yurovsky (1997), From chaotic to 1/f processes in solar mcw-bursts, Astronomy & Astrophysics, 324, P.750-762.
- D.M. Vavriv, V.B. Ryabov, S.A. Sharapov, and H.M. Ito (1996), Chaotic states of weakly and strongly nonlinear oscillators with quasiperiodic excitation, Phys. Rev. E, 53, No.1, P.103-114.
- V.B. Ryabov and D.M. Vavriv, Chaotic instabilities in single- and multi-mode electronic devices, in “Low Temperature and General Plasmas”, edited by M. Miloslavljevich and Z. Petrovic, Nova Science Publishers, Inc., 1996, p.1-13.
- V.B.Ryabov, and H.M.Ito (1995), Multistability and chaos in a spring-block model, Phys. Rev. E, 52, No.6, P.6101-6112.
- V.B. Ryabov, and D.M. Vavriv (1991), Conditions of quasiperidic oscillation destruction in the weakly nonlinear Duffing oscillator, Phys.Lett.A 153, No.8,9. P.431-436.