Dynamic analysis of a fractional order delayed predator–prey system with harvesting

2016 ◽  
Vol 135 (1-2) ◽  
pp. 59-72 ◽  
Author(s):  
Ping Song ◽  
Hongyong Zhao ◽  
Xuebing Zhang
Keyword(s):  
Dynamic Analysis ◽  
Fractional Order ◽  
Predator Prey ◽  
Prey System

scholarly journals Further Results on Bifurcation for a Fractional-Order Predator-Prey System concerning Mixed Time Delays

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhenjiang Yao ◽  
Bingnan Tang
Keyword(s):  
Fractional Order ◽  
Time Delays ◽  
Bifurcation Theory ◽  
Predator Prey ◽  
Mixed Time Delays ◽  
Predator Prey Model ◽  
Prey System ◽  
Change Of Variable ◽  
Set Up ◽  
The Stability

In the present work, we mainly focus on a new established fractional-order predator-prey system concerning both types of time delays. Exploiting an advisable change of variable, we set up an isovalent fractional-order predator-prey model concerning a single delay. Taking advantage of the stability criterion and bifurcation theory of fractional-order dynamical system and regarding time delay as bifurcation parameter, we establish a new delay-independent stability and bifurcation criterion for the involved fractional-order predator-prey system. The numerical simulation figures and bifurcation plots successfully support the correctness of the established key conclusions.

scholarly journals Dynamical behaviors in a discrete fractional-order predator-prey system

Filomat ◽  
2018 ◽  
Vol 32 (17) ◽  
pp. 5857-5874 ◽  
Author(s):  
Yao Shi ◽  
Qiang Ma ◽  
Xiaohua Ding
Keyword(s):  
Numerical Simulations ◽  
Fixed Points ◽  
Fractional Order ◽  
Control Strategies ◽  
Flip Bifurcation ◽  
Predator Prey ◽  
Local Asymptotic Stability ◽  
Dynamical Behaviors ◽  
Prey System ◽  
Theoretical Results

This paper is related to the dynamical behaviors of a discrete-time fractional-order predatorprey model. We have investigated existence of positive fixed points and parametric conditions for local asymptotic stability of positive fixed points of this model. Moreover, it is also proved that the system undergoes Flip bifurcation and Neimark-Sacker bifurcation for positive fixed point. Various chaos control strategies are implemented for controlling the chaos due to Flip and Neimark-Sacker bifurcations. Finally, numerical simulations are provided to verify theoretical results. These results of numerical simulations demonstrate chaotic behaviors over a broad range of parameters. The computation of the maximum Lyapunov exponents confirms the presence of chaotic behaviors in the model.

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