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Vol. 8, No. 5

Vol. 8, No. 5, 2012

Kuznetsov A. P.,  Turukina L. V.,  Kuznetsov S. P.,  Sataev I. R.
Abstract
The conditions are discussed for which the ensemble of interacting oscillators may demonstrate Landau–Hopf scenario of successive birth of multi-frequency regimes. A model is proposed in the form of a network of five globally coupled oscillators, characterized by varying degree of excitement of individual oscillators. Illustrations are given for the birth of the tori of increasing dimension by successive quasi-periodic Hopf bifurcation.
Keywords: synchronization, bifurcations, quasi-periodic dynamics, chaos
Citation: Kuznetsov A. P.,  Turukina L. V.,  Kuznetsov S. P.,  Sataev I. R., Landau–Hopf scenario in the ensemble of interacting oscillators, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 863-873
DOI:10.20537/nd1205001
Emelianova Y. P.,  Mosekilde E.,  Kuznetsov A. P.,  Laugesen J. L.
Abstract
Nephrons (functional units of the kidney) may be described by means of the system of order differential equations. This provides an opportunity to describe dynamics of both the individual and coupled nephrons by using the theory of dynamical systems and the bifurcation theory. Considering a model of a pair of vascular coupled nephrons the present paper examines the effect that the non-identity of nephrons, i. e. non-identity of peak-to-peak variations in their arteriolar radii in autonomous state, has on the behavior of the coupled system. We investigate the appearance possibility of so-called broadband synchronization region, where the stronger nephron starts to suppress the autonomous oscillations of the weaker nephron. We investigate also the appearance possibility of the regime of total oscillator death, where oscillations of both nephrons are abolished.
Keywords: coupled nephrons, total oscillator death, broadband synchronization
Citation: Emelianova Y. P.,  Mosekilde E.,  Kuznetsov A. P.,  Laugesen J. L., Dynamics of coupled nephrons and broadband synchronization, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 875-896
DOI:10.20537/nd1205002
Feoktistov A. V.,  Anishchenko V. S.
Abstract
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
DOI:10.20537/nd1205003
Peregorodova E. N.,  Gerasimova S. A.,  Ryskin N. M.
Abstract
Forced synchronization of a simple model of a three-mode self-oscillator which demonstrates appearance of self-modulation is considered. External driving at the fundamental frequency as well as at the self-modulation satellite frequency is considered. Structures of synchronization domains on the driving frequency — driving amplitude parameter plane and mechanisms of transition to the synchronous regime are investigated for the cases of single-mode and selfmodulated operation of the free-running oscillator.
Keywords: nonlinear oscillations, automodulation, synchronization, mode competition
Citation: Peregorodova E. N.,  Gerasimova S. A.,  Ryskin N. M., On the theory of forced synchronization of self-modulated oscillations, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 913-929
DOI:10.20537/nd1205004
Beletsky V. V.,  Rodnikov A. V.
Abstract
A particle steady motions in vicinity of dynamically symmetric precessing rigid body are studied in assumption that the body gravitational field is modeled as gravitational field of two centers being on imaginary distance. Such particle motion equations are a variant of motion equations of the Generalized Restricted Circular Problem of Three Bodies (GRCP3B). The number of Coplanar Libration Points, i.e. the particle equilibria in the plane passing through the body axis of dynamical symmetry and through the axis of precession are established. (This number is odd and can be equal to 5, 7 or 9). CLPs evolution are studied at changing values of the considered system parameters. Moreover, two Triangular Libration Points, i. e. the particle equilibria in the axis crossing the body mass center orthogonally to axes of precession and dynamical symmetry are found.
Keywords: problem of three bodies, libration points, steady motions, asteroid, regular precession
Citation: Beletsky V. V.,  Rodnikov A. V., Libration Points of the Generalized Restricted Circular Problem of Three Bodies in the case of imaginary distance between attracting centers, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 931-940
DOI:10.20537/nd1205005
Otstavnov E. I.
Abstract
A highly restricted problem of a relative equilibrium for two bodies is considered. They are put into a newtonian gravitational field and tied with inextensible massless fiber. One body is exposed to an air resistance. Stability of relative equilibria is under investigation.
Keywords: space elevator, one-sided restricition, air resistance, relative equilibria, stability
Citation: Otstavnov E. I., A spatial problem of a towed atmospheric probe, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 941-955
DOI:10.20537/nd1205006
Borisov A. V.,  Mamaev I. S.
Abstract
A new integrable system describing the rolling of a rigid body with a spherical cavity over a spherical base is considered. Previously the authors found the separation of variables for this system at the zero level of a linear (in angular velocity) first integral, whereas in the general case it is not possible to separate the variables. In this paper we show that the foliation into invariant tori in this problem is equivalent to the corresponding foliation in the Clebsch integrable system in rigid body dynamics (for which no real separation of variables has been found either). In particular, a fixed point of focus type is possible for this system, which can serve as a topological obstacle to the real separation of variables.
Keywords: integrable system, bifurcation diagram, conformally Hamiltonian system, bifurcation, Liouville foliation, critical periodic solution
Citation: Borisov A. V.,  Mamaev I. S., Topological analysis of one integrable system related to the rolling of a ball over a sphere, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 957-975
DOI:10.20537/nd1205007
Painlevé P.
Abstract
Citation: Painlevé P., Sur les lois du frottement de glissement, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 977-979
DOI:10.20537/nd1205008
Ivanov A. P.
Abstract
Citation: Ivanov A. P., Comments on the P.Painlevé paper “Sur les lois du frottement de glissement”, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 981-984
DOI:10.20537/nd1205009
Abstract
Citation: New books, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 5, pp. 985-988

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