In this paper,we propose a novel fractional-order proportional-derivative(PD)strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with delays.The stability theory of fractional di...In this paper,we propose a novel fractional-order proportional-derivative(PD)strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with delays.The stability theory of fractional differential equations proved that with delays,some explicit conditions for the local asymptotical stability and Hopf bifurcation are given for the controlled fractional-order genetic model.It is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain parameters.In addition,the effect of fractional-order parameter on the dynamical behaviors is shown.Finally,numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller.展开更多
基金the National Natural Science Foundation of China(Nos.61573194,61672298 and 61833005)the Natural Science Foundation of Jiangsu Province of China(No.BK20181389)the Key Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province(Grant.No.2018SJZD1142).
文摘In this paper,we propose a novel fractional-order proportional-derivative(PD)strategy to achieve the control of bifurcation of a fractional-order gene regulatory model with delays.The stability theory of fractional differential equations proved that with delays,some explicit conditions for the local asymptotical stability and Hopf bifurcation are given for the controlled fractional-order genetic model.It is demonstrated that the fractional-order gene regulatory model becomes controllable by adjusting the control gain parameters.In addition,the effect of fractional-order parameter on the dynamical behaviors is shown.Finally,numerical simulations are carried out to testify the validity of the main results and the availability of the fractional-order PD controller.
