Izvestiya VUZ. Applied Nonlinear Dynamics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izvestiya VUZ. Applied Nonlinear Dynamics:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, Volume 24, Issue 3, Pages 38–53 (Mi ivp189)  

APPLIED PROBLEMS OF NONLINEAR OSCILLATION AND WAVE THEORY

Multistability in an ensemble of phase oscillatorswith long-distance couplings

A. V. Shabunin

Saratov State University
Abstract: The work is devoted to investigation of multistability of running waves in a ring of periodic oscillators with diffusive non-local couplings. It analyzes the influence of long-range couplings and their change with distance on the stability of spatially-periodic regimes with different wave numbers.
The research are carried out by numerical (computer) experiments. The system under study is an ensemble of identical phase oscillators. It is, on the one hand the most simple model providing opportunities for analytical studies; on the other hand its properties can be generalized to an arbitrary ensemble of almost harmonic self sustained oscillators.
The studies have shown that multistability is observed in the ensemble of phase oscillators as a set of coexisting modes of waves running along the ring, the every of which characterizing by its own phase-shift between oscillations in the neighboring sites. In the case of stationary or slowly varying couplings a running wave mode remains stable while the total phase shift on the interval of interaction keeps to be less than $\pi/2$. When the couplings are decreased sufficiently fast, the stabilization of the maximum value of the phase shift is observed, so the further increase of range of interaction no longer affects the number of coexisting modes. Thus, the multistability keeps to exist in an ensemble with an arbitrarily distance of interconnection. The study the basins of attraction of the running waves have demonstrated that basins of long-wavelength modes are increased and simultaneously basins of short-wavelength modes are decreased while the range of interconnection grows.
Keywords: Synchronization, multistability, running waves, phase oscillators.
Received: 16.05.2016
Document Type: Article
UDC: 517.9, 621.372
Language: Russian
Citation: A. V. Shabunin, “Multistability in an ensemble of phase oscillatorswith long-distance couplings”, Izvestiya VUZ. Applied Nonlinear Dynamics, 24:3 (2016), 38–53
Citation in format AMSBIB
\Bibitem{Sha16}
\by A.~V.~Shabunin
\paper Multistability in an ensemble of phase oscillatorswith long-distance couplings
\jour Izvestiya VUZ. Applied Nonlinear Dynamics
\yr 2016
\vol 24
\issue 3
\pages 38--53
\mathnet{http://mi.mathnet.ru/ivp189}
Linking options:
  • https://www.mathnet.ru/eng/ivp189
  • https://www.mathnet.ru/eng/ivp/v24/i3/p38
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Izvestiya VUZ. Applied Nonlinear Dynamics
    Statistics & downloads:
    Abstract page:72
    Full-text PDF :23
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024