Amplitude death, oscillation death, and periodic regimes in dynamically coupled Landau–Stuart oscillators with and without distributed delay

Ryan Roopnarain and S. Roy Choudhury

Mathematics and Computers in Simulation (MATCOM), 2021, vol. 187, issue C, 30-50

Abstract: The effects of a distributed ’weak generic kernel’ delay on dynamically coupled Landau–Stuart limit cycle oscillators are considered. The system is closed via the ’linear chain trick’ and the linear stability analysis of the system and conditions for Hopf bifurcations that initiate oscillations are investigated. After reformulation, the effect of the weak generic kernel delay turns out to be mathematically similar to the linear augmentation scheme considered earlier for coupled oscillator systems. For our coupled Landau–Stuart oscillators the distributed delay produces transitions from amplitude death (AD) or oscillation death (OD) to periodic behavior via Hopf Bifurcations, with the delayed limit cycle shrinking or growing as the delay is varied towards or away from the bifurcation point respectively. The transition from AD to OD occurs here via a supercritical pitchfork bifurcation, as also seen previously for some other couplings. In addition, the dynamically coupled Landau–Stuart system has a secondary limit cycle emerging within the OD parameter regime, in contrast to other couplings and systems studied earlier.

Keywords: Complex bifurcation sequences; Amplitude death; Oscillation death; Pitchfork and Hopf bifurcations; Distributed delay effects; Comparisons to other couplings (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475421000458
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:187:y:2021:i:c:p:30-50

DOI: 10.1016/j.matcom.2021.02.006

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().