Controlling bifurcation in a delayed fractional predator-prey system with incommensurate orders

A novel delayed fractional-order gene regulatory network model is proposed in this paper. Firstly, the sum of delays is chosen as the bifurcation parameter, the conditions of the existence for the Hopf bifurcation are obtained by analyzing the associated characteristic equation. Then, it is the first time that a hybrid controller is designed to control the Hopf bifurcation for the proposed network. It is demonstrated that both fractional order and feedback gain can effectively control the dynamics of such network, the stability domain can be extended under the small fractional order or feedback gain. The controller is enough to delay the onset of the Hopf bifurcation and achieve some desirable dynamical behaviors by changing the appropriate order or feedback gain. Finally, numerical simulations are employed to justify the validity of our theoretical analysis.

Hybrid control on bifurcation for a delayed fractional gene regulatory network

Hopf bifurcation analysis of a delayed fractional-order genetic regulatory network model

Effects of time delays on stability and Hopf bifurcation in a fractional ring-structured network with arbitrary neurons

In this work, a fractional-order prey-predator system with fear effect of predator on prey population and group defense has been proposed. The existence and uniqueness of the system have been studied. Non-negativity and boundedness are also theoretically demonstrated. Analysis of local stability with examination of saddle-node and Hopf bifurcation at equilibrium points are performed by the help of numerical simulations along with analytical study. All the numerical simulations are performed using MATLAB and MAPLE.

https://link.springer.com/content/pdf/10.1007/s40435-020-00626-x.pdf

A prey-predator fractional order model with fear effect and group defense

In this paper, a new fractional-order hyperchaotic system based on the Lorenz system is presented. The chaotic behaviors are validated by the positive Lyapunov exponents. Furthermore, the fractional Hopf bifurcation is investigated. It is found that the system admits Hopf bifurcations with varying fractional order and parameters, respectively. Under different bifurcation parameters, some conditions ensuring the Hopf bifurcations are proposed. Numerical simulations are given to illustrate and verify the results.

Xiang Li

Papers

Hopf bifurcation analysis of a new commensurate fractional-order hyperchaotic system