Ghost attractors in fractional order unified chaotic blinking systems
ZHU Wen-hao
ZENG Cai-bin
Abstract：Little seems to be known about the dynamics of the fractional order stochastically blinking systems.In this paper,we consider the complex dynamics of fractional order unified chaotic blinking systems coupled topologically nonequivalent subsystems.Firstly,we prove the conditions for local stability and Hopf bifurcation of the fractional order unified chaotic system.Then we analyze the change in the dynamical behavior with the increasing of the period of stochastic switching and fractional order.We demonstrate that under special switching probabilities,the fractional order unified chaos blinking system exhibits ghost attractor.Fast switching between a Lorenz attractor and a Chen attractor yields an attractor which may rapidly deviate from the Lü attractor which acts as a ghost chaotic attractor as the switching period increases.Under the case of non fast switching,the degree of deviation between the non-stationary attractor and the ghost attractor will remain stable with increasing switching period.Additionally,the deviation degree of these two attractors depends on the order of the fractional operator.Based on ergodic property,we carry out the numerical approximations of the invariant measures of the blinking and averaged systems,resulting in the estimate of a non-stationary and ghost attractors' proximity.
Keywords：fractional calculusblinking systemchaosHopf bifurcation
Publication Date：2025-06-30
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：8( 1200-1207 )