Stochastic Dynamics

Анищенко, В. С.; Astakhov, V. V.; Вадивасова, Т. Е.; Neiman, Alexander; Schimansky‐Geier, Lutz

doi:10.1007/978-3-540-38168-6_3

Cited by 81 publications

(126 citation statements)

References 284 publications

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“…3 Model of two double spherical pendula 3. 4 Three degrees of freedom discontinuous model 3.4.1 Energy balance of the clocks' pendula 3.4.2 Energy balance of the beam and whole system (26,27) 3. 5 Three degrees of freedom model with van der Pol's friction 3.…”

Section: Contentsmentioning

confidence: 99%

“…2 , β III =360 o -β 3 , β IV =β 4 , β V =360 o -β 5 [deg] -phase shift between pendula; -initial values of displacement and velocity of the beam;…”

Section: Contentsmentioning

confidence: 99%

“…As the period of this function T m is larger than T (the period of pendula' oscillations in the case when beam M is at rest) this type of generalized synchronization is called a long period synchronization. The long period synchronization can be a special case of n:m synchronization observed in the selfexcited continuous systems [4,8]. Since the system (27,28) is discontinuous and we have not proved the existence of the quasiperiodic solution on the torus in it we decide to use other name.…”

Section: Synchronization Of Two Identical Pendulamentioning

confidence: 99%

“…(118-120)) can be generalized to any number of pendula synchronized in five clusters. Substituting the total masses of clusters instead of pendulum masses m [1][2][3][4][5] one gets the equations which allow the estimation of the phase shifts between clusters.…”

Section: (B) Four Clocks (N=4)mentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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Abstract:In this report we recall the famous Huygens' experiment which gave the first evidence of the synchronization phenomenon. We consider the synchronization of two clocks which are accurate (show the same time) but have pendulawith different masses. It has been shown that such clocks hanging on the same beam can show the almost complete (in-phase) and almost antiphase synchronizations. By almost complete and almost antiphase synchronization we defined the periodic motion of the pendula in which the phase shift between the displacements of the pendula is respectively close (but not equal) to 0 or π.We give evidence that almost antiphase synchronization was the phenomenon observed by Huygens in XVII century. We support our numerical studies by considering the energy balance in the system and showing how the energy is transferred between the pendula via oscillating beam allowing the pendula's synchronization. Additionally we discuss the synchronization of a number of different pendulum clocks hanging from a horizontal beam which can roll on the parallel surface. It has been shown that after a transient, different types of synchronization between pendula can be observed;(i) the complete synchronization in which all pendula behave identically, (ii) pendula create three or five clusters of synchronized pendula. We derive the equations for the estimation of the phase differences between phase synchronized clusters. The evidence, why other configurations with a different number of clusters are not observed, is given.

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Section: Contentsmentioning

confidence: 99%

“…2 , β III =360 o -β 3 , β IV =β 4 , β V =360 o -β 5 [deg] -phase shift between pendula; -initial values of displacement and velocity of the beam;…”

Section: Contentsmentioning

confidence: 99%

Section: Synchronization Of Two Identical Pendulamentioning

confidence: 99%

Section: (B) Four Clocks (N=4)mentioning

confidence: 99%

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Synchronization of clocks

et al. 2012

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“…The recent influence of the theory of networks [1][2][3] on the classic field of coupled oscillatory units [4] has led to the discovery of a plethora of novel phenomena, especially when the coupling between units becomes more sophisticated, mimicking naturally interacting systems. Among the complex oscillatory patterns that may emerge, are the so-called "chimera states" [5,6], which have recently attracted a lot of attention.…”

Section: Introductionmentioning

confidence: 99%

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

et al. 2015

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We study numerically the development of chimera states in networks of nonlocally coupled oscillators whose limit cycles emerge from a Hopf bifurcation. This dynamical system is inspired from population dynamics and consists of three interacting species in cyclic reactions. The complexity of the dynamics arises from the presence of a limit cycle and four fixed points. When the bifurcation parameter increases away from the Hopf bifurcation the trajectory approaches the heteroclinic invariant manifolds of the fixed points producing spikes, followed by long resting periods. We observe chimera states in this spiking regime as a coexistence of coherence (synchronization) and incoherence (desynchronization) in a one-dimensional ring with nonlocal coupling, and demonstrate that their multiplicity depends both on the system and the coupling parameters. We also show that hierarchical (fractal) coupling topologies induce traveling multichimera states. The speed of motion of the coherent and incoherent parts along the ring is computed through the Fourier spectra of the corresponding dynamics.

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Complex oscillations in systems subject to periodic perturbation

Nikitina

2011

Int Appl Mech

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The principle of antisymmetry that gives rise to closed orbits of limit cycles and quasiperiodic trajectories of stable oscillations is formulated. The conditions of attraction of synchronized limit cycle as a whole are established. A bifurcational phase portrait of a synchronized limit cycle is considered. It is shown that the subharmonic capture of the limit cycle with period multiplication involves loss of symmetry and preservation of attraction

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Stochastic Dynamics

Cited by 81 publications

References 284 publications

Synchronization of clocks

Synchronization of clocks

Chimera states in population dynamics: Networks with fragmented and hierarchical connectivities

Complex oscillations in systems subject to periodic perturbation

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