TY - JOUR
T1 - An Extremely Simple Chaotic System with Infinitely Many Coexisting Attractors
AU - Lai, Qiang
AU - Kamdem Kuate, Paul Didier
AU - Liu, Feng
AU - Iu, Herbert Ho Ching
N1 - Publisher Copyright:
© 2004-2012 IEEE.
PY - 2020/6
Y1 - 2020/6
N2 - The discovery of simple chaotic systems with complex dynamics has always been an interesting research work. This brief aims to construct an extremely simple chaotic system with infinitely many coexisting chaotic attractors. The system consists of five terms with two nonlinearities, and has an infinite number of unstable equilibria owing to its sinusoidal nonlinearity. The most prominent feature of the system is that it coexists infinitely many chaotic attractors for different initial values and fixed system parameters. To our best knowledge, there is no 3-D system with such a simple mathematical model can produce infinitely many coexisting chaotic attractors. The phenomenon of coexisting attractors of the new system is numerically investigated. The circuit and microcontroller-based implementation of the system are presented as well.
AB - The discovery of simple chaotic systems with complex dynamics has always been an interesting research work. This brief aims to construct an extremely simple chaotic system with infinitely many coexisting chaotic attractors. The system consists of five terms with two nonlinearities, and has an infinite number of unstable equilibria owing to its sinusoidal nonlinearity. The most prominent feature of the system is that it coexists infinitely many chaotic attractors for different initial values and fixed system parameters. To our best knowledge, there is no 3-D system with such a simple mathematical model can produce infinitely many coexisting chaotic attractors. The phenomenon of coexisting attractors of the new system is numerically investigated. The circuit and microcontroller-based implementation of the system are presented as well.
KW - Chaotic system
KW - circuit implementation
KW - coexisting attractors
KW - initial conditions
KW - microcontroller
UR - http://www.scopus.com/inward/record.url?scp=85085930957&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85085930957&partnerID=8YFLogxK
U2 - 10.1109/TCSII.2019.2927371
DO - 10.1109/TCSII.2019.2927371
M3 - Article
AN - SCOPUS:85085930957
SN - 1549-7747
VL - 67
SP - 1129
EP - 1133
JO - IEEE Transactions on Circuits and Systems II: Express Briefs
JF - IEEE Transactions on Circuits and Systems II: Express Briefs
IS - 6
M1 - 8758327
ER -