Chen Jufeng

Shijiazhuang Tiedao University · Department of Mathematics and Physics

The stability and existence conditions of Hopf bifurcation of a commensurate fractional-order van der Pol oscillator with time-delayed feedback are studied. Firstly, the necessary and sufficient conditions for the asymptotic stability of the equilibrium point of fractional-order van der Pol oscillator with linear displacement feedback are obtained,...

The primary resonance of van der Pol oscillator under fractional-order delayed negative feedback and forced excitation is studied. Firstly, the approximate analytical solution is obtained based on the averaging method, and it could be found that the fractional-order delayed feedback has not only the property of delayed velocity feedback but also th...

The integer-order and fractional-order Brusselators with two different time scales are studied. The double-Hopf bursting oscillation is observed in Brusselator with periodic perturbation under some parameter conditions. Based on slow-fast analysis and bifurcation theory, the generation mechanism of periodic bursting oscillation is presented in deta...

The fractional-order Belousov-Zhabotinsky (BZ) reaction with different time scales is investigated in this paper. Based on the stability theory of fractional-order differential equation, the critical condition of Hopf bifurcation with two parameters in fractional-order BZ reaction is discussed. By comparison of the fractional-order and integer-orde...

A simple, but very accurate analytical method for forced Mathieu oscillator is proposed, the idea of which is based on the method of variation of parameter. Assuming that the time-varying parameter in Mathieu oscillator is constant, one could easily obtain its accurately analytical solution. Then the approximately analytical solution for Mathieu os...