Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 172, Issue -, Pages 321-340Publisher
ELSEVIER
DOI: 10.1016/j.matcom.2019.11.009
Keywords
Chaotic Caputo fractional-order system; Hopf bifurcation; Stability of equilibria; Chaos control and synchronization
Ask authors/readers for more resources
This paper deals with the stability and bifurcation of equilibria in a new chaotic fractional-order system in the sense of the Caputo fractional derivative with the chaos entanglement function. We derive conditions under which the system undergoes a Hopf bifurcation and obtain critical parameter value in the Hopf bifurcation. Moreover, the linear feedback control technique is used to control and stabilize the system to equilibrium point in order to eliminate the chaotic vibration. We then design control laws to synchronize two identical chaotic fractional-order systems. Furthermore, by means of numerical simulation, we support the validity of analytical results and reveal more dynamical behaviors consisting chaos, local bifurcation, limit cycles, quasiperiodic and asymptotic stability behaviors. We further emphasize that the order of fractional derivative plays significant roles as the chaos controlling parameter and the Hopf bifurcation parameter. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B. V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available