Chunbiao Li∗,†,§, Yuxuan Peng†,‡,¶ and Ze
Tao†,‡ ∗
School of Artificial Intelligence,
Nanjing University of Information Science and Technology,
Nanjing 210044, P. R. China
†
Jiangsu Collaborative Innovation Center of Atmospheric
Environment and Equipment Technology (CICAEET),
Nanjing University of Information Science and Technology,
Nanjing 210044, P. R. China
‡
Jiangsu Key Laboratory of Meteorological Observation and
Information Processing, Nanjing University of Information
Science and Technology, Nanjing 210044, P. R. China
§
goontry@126.com
§
chunbiaolee@nuist.edu.cn
¶
alexpengcn@foxmail.com
lebrontaoze@163.com
Julien Clinton Sprott
Department of Physics,
University of Wisconsin−Madison,
Madison, WI 53706, USA
sprott@physics.wisc.edu
Sajad Jafari
Biomedical Engineering Faculty,
Amirkabir University of Technology,
424 Hafez Ave, 15875-4413, Tehran, Iran
sajadjafari83@gmail.com
Received March 18, 2020; Revised October 18, 2020
Equilibria are a class of attractors that host inherent stability in
a dynamic system. Infinite
number of equilibria and chaos sometimes coexist in a system with
some connections. Hidden
chaotic attractors exist independent of any equilibria rather than
being excited by them. However, the equilibria can modify, distort,
eliminate, or even instead coexist with the chaotic
attractor depending on the distance between the equilibria and
chaotic attractor. In this paper,
chaotic systems with infinitely many equilibria are considered and
explored. Extra surfaces of
equilibria are introduced into the chaotic flows, showing that a
chaotic system can maintain its
basic dynamics if the newly added equilibria do not intersect the
original attractor. The offset boostable plane of equilibria
rescales the frequency of the chaotic oscillation with an almost
linearly modified largest Lyapunov exponent or conversely drives the
system into periodic oscillation, even ending in a divergent state.
Furthermore, additional infinite number of equilibria
or even a solid space of equilibria are safely nested into the
chaotic system without destroying the original dynamics, which
provides an alternate permanent location for a dynamical system.
A circuit simulation agrees with the numerical calculation.
Ref:
C.
Li, Y. Peng, Z. Tao, J. C. Sprott, and S. Jafari, International
Journal of
Bifurcation and Chaos 31, 2130014-1-17 (2021).