TY - JOUR
T1 - Mathematical and numerical analysis of the dynamical behavior of chen oscillator
AU - Nuñez-Perez, Jose Cruz
AU - Adeyemi, Vincent Ademola
AU - Sandoval-Ibarra, Yuma
AU - Serrato-Andrade, Rodrigo Yaoctzin
AU - Cardenas-Valdez, Jose Ricardo
AU - Tlelo-Cuautle, Esteban
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - Over the years, chaos has been an important subject of interest to many researchers. Many chaotic oscillators have been proposed in literature. The oscillating and the possible stability in chaotic systems could be applied as fundamental tools in developing real world applications in several disciplines such as engineering, telecommunication, medicine, etc. In this work, the Chen oscillator dynamic and stability behavior are studied by applying mathematical and numerical analyses to investigate the equilibria, eigenvalues, Lyapunov exponents and bifurcation diagrams. The eigenvalues obtained show that the Chen oscillator is unstable at the equilibrium points examined while the maximum Lyapunov exponent obtained confirms its chaotic nature. Also, the bifurcation diagrams show the stability of the Chen system with the three system parameters. The results show that bifurcation with parameter b gives the longest period of stability.
AB - Over the years, chaos has been an important subject of interest to many researchers. Many chaotic oscillators have been proposed in literature. The oscillating and the possible stability in chaotic systems could be applied as fundamental tools in developing real world applications in several disciplines such as engineering, telecommunication, medicine, etc. In this work, the Chen oscillator dynamic and stability behavior are studied by applying mathematical and numerical analyses to investigate the equilibria, eigenvalues, Lyapunov exponents and bifurcation diagrams. The eigenvalues obtained show that the Chen oscillator is unstable at the equilibrium points examined while the maximum Lyapunov exponent obtained confirms its chaotic nature. Also, the bifurcation diagrams show the stability of the Chen system with the three system parameters. The results show that bifurcation with parameter b gives the longest period of stability.
KW - Chaos
KW - Chen oscillator
KW - Lyapunov exponent
KW - Mathematical and numerical analysis
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=85073929967&partnerID=8YFLogxK
U2 - 10.1007/s40435-019-00573-2
DO - 10.1007/s40435-019-00573-2
M3 - Artículo
AN - SCOPUS:85073929967
SN - 2195-268X
VL - 8
SP - 386
EP - 395
JO - International Journal of Dynamics and Control
JF - International Journal of Dynamics and Control
IS - 2
ER -