Bifurcation delay, travelling waves and chimera-like states in a network of coupled oscillators
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part of Springer Nature, 2020 https://doi.org/10.1140/epjst/e2020-900192-x
THE EUROPEAN PHYSICAL JOURNAL SPECIAL TOPICS
Regular Article
Bifurcation delay, travelling waves and chimera-like states in a network of coupled oscillators Vaibhav Varshney1 , Suresh Kumarasamy1,a , Bibhu Biswal2 , and Awadhesh Prasad1 1 2
Department of Physics and Astrophysics, University of Delhi, Delhi-110007, India Cluster Innovation Centre, University of Delhi, University of Delhi, Delhi-110007, India Received 6 September 2019 / Accepted 8 June 2020 Published online 28 September 2020 Abstract. We report novel bifurcation delays and chimera-like states in a network of driven FitzHugh-Nagumo (FHN) oscillators, where each oscillator can rotate either clockwise or anticlockwise. Slow variation of the time-dependent parameter of FHN oscillator near the bifurcation point leads to a delay in the bifurcation. The time delay in the bifurcation is independent of the direction of rotation of the system (clockwise or anticlockwise rotation). When the FHN oscillators are coupled via dissimilar variables, then bifurcation delay in the anticlockwise rotating oscillator changes, creating chimera-like structures and also travelling waves at certain coupling strength. Bifurcation preponement is also observed for other range of coupling strengths. Similar results are also observed in networks of van der Pol and Landau-Stuart oscillators suggesting that the phenomenon is general rather than specific to coupled FHN systems.
1 Introduction Exploring the dynamics of complex networks has been a focus area of research. Recently a range of interesting dynamical behaviour, such as synchronization [1–3], chimera states [4], amplitude death [5–9] etc., have been studied in coupled systems. The collective behaviour of the network depends on the properties of individual oscillators such as parameters, dynamics and bifurcation points among others. Time dependence of a parameter may cause novel changes in the bifurcation diagram and as a result the dynamics of the network differ significantly from that with stationary control parameters [10–14], e.g., weight of any running fuel vehicle as a function of time [15,16] or catalytic activities in a chemical reactor slowly declining because of the chemical erosion and decreasing the reactor performance [17,18]. One important feature of systems with time-varying parameter is that bifurcation point is shifted and occurs at a later time (delayed bifurcations) or at an earlier time (preponed bifurcation) [17,18]. Hence, the dynamics predicted based on the bifurcation analysis with the time-independent parameter may lead to different dynamics than the actual a
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The European Physical Journal Special Topics
dynamics. These phenomena are of interest for their applications in lasers [19], fluid convection [20], electronic circuits [21], and bistable chemical reaction [22,23]. The collective behaviour of ensembles of interacting oscillators has also been of considerable interest in diverse
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