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    Vadim Anishchenko

    Vadim Anishchenko
    Astrakhanskaya 83, 410026, Saratov, Russia
    Saratov State University, Russia

    Department of Physics, Saratov State University
    Head of Radiophysics and Nonlinear Dynamics Chair, Saratov State University, Russia

    Born: October 21, 1943
    1961-1966: student of Saratov State University, Russia.
    1968-1970: Post-graduate (Ph.D.) student, Saratov State University, Russia


    1968-1970: Post-graduate student, State University, Saratov, Russia
    1970-1987: Assistent, First teacher, Associate professor,State University, Saratov, Russia
    1987-1987: Professor, Humboldt University, Berlin
    1987-1988: Professor, State University, Saratov, Russia
    Since 1988: Head of Radiophysics and Nonlinear Dynamics Chair, State University, Saratov, Russia


    1970: Ph.D., Saratov State University, Russia
    1987: Doctor of Sciences, Saratov State University, Russia
    1989: Professor of Radiophysics and Nonlinear Dynamics Chair, Saratov State University, Russia
    1994: Scientific Grant of the President of Russia and  Russian Academy of Sciences
    1994: Soros Professor
    1995: Honored Man of Science of Russia
    1995: Corresponding Member of International Academy of Informatization (OON)
    1997: Corresponding Member of Russian Academy of Natural Sciences


    Semenova N. I., Anishchenko V. S.
    We consider the dynamics of a ring of nonlocally coupled logistic maps when varying the coupling coefficient. We introduce the coupling function, which characterizes the impact of nonlocal neighbors and study its dynamics together with the dynamics of the whole ensemble. Conditions for the transition from complete chaotic synchronization to partial one are analyzed and the corresponding theoretical estimation of the bifurcation parameter $\sigma$ is given. Conditions for the appearance of phase and amplitude chimera states are also studied.
    Keywords: chimera states, nonlocal coupling, chaotic synchronization, desynchronization, onedimensional ensemble
    Citation: Semenova N. I., Anishchenko V. S.,  Coherence-incoherence transition with appearance of chimera states in a onedimensional ensemble, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 3, pp.  295-309
    Boev Y. I., Strelkova G. I., Anishchenko V. S.
    The local theory of Poincaré recurrences is applied to estimate pointwise and information dimensions of chaotic attractors in two-dimensional nonhyperbolic and hyperbolic maps. It is shown that the local pointwise dimension can be defined by calculating the mean recurrence times depending on the return vicinity size. The values of pointwise, information, capacity, and Lyapunov dimensions are compared. It is also analyzed how the structure of attractors can affect the calculation of the dimensions.
    Keywords: Poincaré recurrence, probability measure, fractal dimension
    Citation: Boev Y. I., Strelkova G. I., Anishchenko V. S.,  Estimating dimensions of chaotic attractors using Poincaré recurrences, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 3, pp.  475-485
    Semenova N. I., Anishchenko V. S.
    In the present work we analyze the statistics of a set that is obtained by calculating a stroboscopic section of phase trajectories in a harmonically driven van der Pol oscillator. It is shown that this set is similar to a linear shift on a circle with an irrational rotation number, which is defined as the detuning between the external and natural frequencies. The dependence of minimal return times on the size ε of the return interval is studied experimentally for the golden ratio. Furthermore, it is also found that in this case, the value of the Afraimovich–Pesin dimension is $\alpha_c = 1$.
    Keywords: Poincaré recurrence, Afraimovich–Pesin dimension, Fibonacci stairs, circle map, van der Pol oscillator
    Citation: Semenova N. I., Anishchenko V. S.,  Poincaré recurrences in a stroboscopic section of a nonautonomous van der Pol oscillator, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 2, pp.  149-156
    Boev Y. I., Semenova N. I., Anishchenko V. S.
    The statistics of Poincaré recurrences is studied numerically in a one-dimensional cubic map in the presence of harmonic and noisy excitations. It is shown that the distribution density of Poincare recurrences is periodically modulated by the harmonic forcing. It is substantiated that the theory of the Afraimovich–Pesin dimension can be applied to a nonautonomous map for both harmonic and noisy forcings. It is demonstrated that the relationship between the AP-dimension and Lyapunov exponents is violated in the nonautonomous system.
    Keywords: Poincaré recurrence, probability measure, Afraimovich–Pesin dimension
    Citation: Boev Y. I., Semenova N. I., Anishchenko V. S.,  Statistics of Poincaré recurrences in nonautonomous chaotic 1D map, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 1, pp.  3-16
    Feoktistov A. V., Anishchenko V. S.
    Phenomenon of coherence resonance and external synchronization of noise-induced stochastic oscillations in hard excitation oscillator are studied by means of natural experiments. Regions of synchronization on parameter plane are constructed. Experiments on synchronization in hard excitation oscillator without noise are carried out.
    Keywords: coherence resonance, synchronization, noise-induced oscillators, hard excitation oscillator
    Citation: Feoktistov A. V., Anishchenko V. S.,  Coherence resonance and synchronization of stochastic self-sustained oscillations in hard excitation oscillator, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp.  897-911
    Anishchenko V. S., Semenova N. I., Astakhov S. V., Boev Y. I.
    The concept of a local fractal dimension has been introduced in the framework of the average Poincaré recurrence time numerical analysis in an $\varepsilon$-vicinity of a certain point. Lozi and Hénon maps have been considered. It has been shown that in case of Lozi map the local dimension weakly depends on the point on the attractor and its value is close to the fractal dimension of the attractor. In case of a quasi attractor observed in both Hénon and Feugenbaum systems the local dimension significantly depends on both the diameter and the location of the $\varepsilon$-vicinity. The reason of this strong dependency is high non-homogenity of a quasi-attractor which is typical for non-hyperbolic chaotic attractors.
    Keywords: Poincaré recurrence, attractor dimension
    Citation: Anishchenko V. S., Semenova N. I., Astakhov S. V., Boev Y. I.,  Poincaré recurrences time and local dimension of chaotic attractors, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 3, pp.  449-460
    Anishchenko V. S., Astakhov S. V., Boev Y. I., Kurths J.
    Statistical properties of Poincaré recurrences in a two-dimensional map with chaotic non-strange attractor have been studied in numerical simulations. A local and a global approaches were analyzed in the framework of the considered problem. It has been shown that the local approach corresponds to Kac’s theorem including the case of a noisy system in certain conditions which have been established. Numerical proof of theoretical results for a global approach as well as the Afraimovich–Pesin dimension calculation are presented.
    Keywords: Poincaré recurrence, attractor dimension, Afraimovich–Pesin dimension
    Citation: Anishchenko V. S., Astakhov S. V., Boev Y. I., Kurths J.,  Poincaré recurrences in a system with non-strange chaotic attractor, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 1, pp.  29-41
    Anishchenko V. S.
    In memory of Leonid Pavlovich Shilnikov
    2012, Vol. 8, No. 1, pp.  187-190
    Citation: Anishchenko V. S.,  In memory of Leonid Pavlovich Shilnikov, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 1, pp.  187-190
    Anishchenko V. S., Vadivasova T. E., Strelkova G. I.
    In the present paper autonomous and nonautonomous oscillations of dynamical and stochastic systems are analyzed in the framework of common concepts. The definition of an attractor is introduced for a nonautonomous system. The definitions of self-sustained oscillations and a self-sustained oscillatory system is proposed, that generalize A.A.Andronov’s concept introduced for autonomous systems with one degree of freedom.
    Keywords: self-sustained oscillations, dynamical chaos, attractor, fluctuations
    Citation: Anishchenko V. S., Vadivasova T. E., Strelkova G. I.,  Self-sustained oscillations of dynamical and stochastic systems and their mathematical image — an attractor, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 1, pp.  107-126
    Anishchenko V. S., Astakhov S. V., Vadivasova T. E., Feoktistov A. V.
    The effect of synchonization has been studied in a system of two coupled Van der Pol oscillators under external harmonic force. The bifurcation analysis has been carried out using the phase approach. The mechanisms of complete and partial synchronization have been established. The main type of bifurcation described in the paper is the saddle-node bifurcation of invariant curves that corresponds to the saddle-node bifurcation of two-dimensional tori in the complete system of differential equations for the dynamical system under study. We illustrate the bifurcational mechanisms obtained from numerical experiment by the results of physical experiment. The synchronization phenomenon in the vicinity of resonances on a torus with winding numbers 1 : 1 and 1 : 3 is considered in the physical experiment.
    Keywords: limit cycle, torus, saddle-node bifurcation, synchronization
    Citation: Anishchenko V. S., Astakhov S. V., Vadivasova T. E., Feoktistov A. V.,  Numerical and experimental study of external synchronization of two-frequency oscillations, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 2, pp.  237-252
    Zakharova A. S., Vadivasova T. E., Anishchenko V. S.
    We investigate effective diffusion coefficient of instantaneous phase of chaotic self-sustained oscillations and its connection with synchronization threshold. It is showed that effective phase diffusion coefficient in contrast to maximal Lyapunov exponent allows to distinguish the regions of spiral and funnel attractor. We ascertain that synchronization threshold of chaos is in order-of-magnitude agreement with the value of diffusion coefficient divided by the mean frequency of self-sustained oscillations.
    Keywords: chaotic self-sustained oscillations, synchronization threshold, effective diffusion coefficient of instantaneous phase
    Citation: Zakharova A. S., Vadivasova T. E., Anishchenko V. S.,  The interconnection of synchronization threshold with effective diffusion coefficient of instantaneous phase of chaotic self-sustained oscillations, Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 2, pp.  160-180
    Anishchenko V. S., Nikolaev S. M.
    We investigate synchronization of a resonant limit cycle on a two dimensional torus by an external harmonic signal. The regime of resonant limit cycle is realized in a system of two coupled Van der Pol oscillators, we consider the resonances 1:1 and 1:3. We analyse the influence of the generators coupling strength. We show, that generally the effect of synchronization of a resonant limit cycle on torus is followed by the distruction of the resonance in the system, next one of the basic frequencies of the system becomes locked, and then another. We consider the bifurcation mechanism of synchronization effect.
    Keywords: limit cycle, torus, saddle-node bifurcation, synchronization
    Citation: Anishchenko V. S., Nikolaev S. M.,  Synchronizationmechanisms of resonant limit cycle on two-dimensional torus, Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 1, pp.  39-56
    Anishchenko V. S., Nikolaev S. M.
    We propose a new autonomous dynamical system of dimension $N = 4$ that demonstrates the regime of stable two-frequency motions. It is shown that system of two generators of quasiperiodic motions with symmetric coupling can realize motions on four-dimensional torus with resonant structures on it in the form of three- and two-dimensional torus. We show that with increase of noise intensity the higher the dimension of torus the faster it is destroyed.
    Keywords: quasiperiodic motions, synchronization, chaos
    Citation: Anishchenko V. S., Nikolaev S. M.,  Stability, synchronization and destruction of quasiperiodic motions, Rus. J. Nonlin. Dyn., 2006, Vol. 2, No. 3, pp.  267-278

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