Master stability in the presence of megastability: Emergence
of oscillatory synchronization patterns
Karthikeyan Rajagopal a,b, Arezoo Firouzeh c, Mahtab Mehrabbeik
c,
Sajad Jafari c,d,*, Julien Clinton Sprott e
a Center for Research, Easwari Engineering College,
Chennai, India
b Center for Research, SRM TRP Engineering College, Trichy,
India
c Department of Biomedical Engineering, Amirkabir
University of Technology (Tehran Polytechnic), Tehran, Iran
d Health Technology Research Institute, Amirkabir
University of Technology (Tehran Polytechnic), Tehran, Iran
e Department of Physics, University of Wisconsin, Madison,
WI 53706, USA
A B S T R A C T
In this paper, we present the master stability
function (MSF) analysis of synchronization in megastable
dynamical systems—those with a countable infinity of coexisting
attractors—across three benchmark oscillators (cabbage, simplest
sinusoidal, and tanh–exponential) and four single coupling
channels. For attractors selected by initial conditions, we
quantify how dissipativity and external forcing shape stability
on the synchronization manifold. While inner (more dissipative)
attractors generally admit broader stability, the most striking
outcome is the emergence of finely oscillatory MSF curves that
partition the coupling axis into interleaved, narrow intervals.
Unlike conventional MSF patterns, these repeated sign changes
persist over wide coupling ranges, producing highly fragmented
stability windows rather than a single contiguous region. This
unprecedented phenomenon survives under forcing and depends
strongly on the coupling pathway, revealing an unusually
delicate balance between local megastable dynamics and network
embedding. By characterizing this structured alternation of
stable and unstable bands, the study clarifies why achieving
collective synchrony in megastable regimes may be inherently
challenging and points to targeted choices of attractor and
coupling channel as key levers for
future network designs.
Ref: K. Rajagopal, A. Firouzeh, M. Mehrabbeik,
S. Jafari, and J. C. Sprott,Chaos, Solitons and Fractals 211,
118791-1-15 (2026)
The