Multistability in a 3D Circulant Chaotic Flow: The Circulant
Symmetry of Coexisting Dynamics
Karthikeyan Rajagopal
Center for Research, SRM Easwari Engineering College,
Chennai 600089, India
Center for Cognitive Science,
Trichy SRM Medical College Hospital and Research Center,
Trichy 621105, India
rkarthiekeyan@gmail.com
Fahimeh Nazarimehr ;z and Sajad Jafari ;y;x
Department of Biomedical Engineering,
Amirkabir University of Technology (Tehran Polytechnic),
Tehran 1591634311, Iran
yHealth Technology Research Institute,
Amirkabir University of Technology (Tehran Polytechnic),
Tehran 1591634311, Iran
zf nazarimehr@aut.ac.ir; fahimenazarimehr@yahoo.com
xsajadjafari@aut.ac.ir
Julien C. Sprott
Department of Physics, University of Wisconsin{Madison,
Madison, WI 53706, USA
csprott@wisc.edu
Received May 21, 2025; Accepted July 27, 2025; Published October
16, 2025
In this paper, a novel chaotic ow exhibiting
circulant symmetry is modeled and analyzed. The chaotic
ow's dynamical behavior is thoroughly investigated, revealing
that it is dissipative over the studied parameter values. A
basic equilibrium analysis shows that four of the system's
equilibrium points are stable. Notably, the system exhibits two
distinct sets of three coexisting chaotic attractors, each set
displaying circulant symmetry. To the best of our knowledge,
such a system has not been previously reported in the
literature. Bifurcation analysis with respect to all three
system parameters con rms the rich dynamical behavior, supported
by corresponding Lyapunov exponent spectra. The basins of
attraction reveal rare V-shaped boundaries, adding to the
system's uniqueness. Furthermore, the circulant symmetry is
clearly reected in the basins of attraction of the coexisting
attractors.
Ref: K. Rajagopal, F. Nazarimehr, S. Jafari and J. C. Sprott,
International Journal of Bifurcation and Chaos 35,
250004-1-13 (2025)