Stability and Hopf bifurcation analysis of a biotic resource enrichment on a prey predator population in fractional-order system

2021 ◽  
Author(s):  
Abiodun Ezekiel Owoyemi ◽  
Ibrahim Mohammed Sulaiman ◽  
Salisu Sadiya Muhammad ◽  
Oluwatayo Olatunde Oni ◽  
Olukayode Williams Okedokun
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Bifurcation Analysis ◽  
Fractional Order System ◽  
Order System ◽  
Predator Population ◽  
Biotic Resource

scholarly journals Complexity and Hopf Bifurcation Analysis on a Kind of Fractional-Order IS-LM Macroeconomic System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650181 ◽  
Author(s):  
Junhai Ma ◽  
Wenbo Ren
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Dynamic Characteristics ◽  
Fractional Order System ◽  
Order System ◽  
Complex Dynamic ◽  
Macroeconomic Regulation And Control ◽  
And Control ◽  
System Order ◽  
Macroeconomic Environment

On the basis of our previous research, we deepen and complete a kind of macroeconomics IS-LM model with fractional-order calculus theory, which is a good reflection on the memory characteristics of economic variables, we also focus on the influence of the variables on the real system, and improve the analysis capabilities of the traditional economic models to suit the actual macroeconomic environment. The conditions of Hopf bifurcation in fractional-order system models are briefly demonstrated, and the fractional order when Hopf bifurcation occurs is calculated, showing the inherent complex dynamic characteristics of the system. With numerical simulation, bifurcation, strange attractor, limit cycle, waveform and other complex dynamic characteristics are given; and the order condition is obtained with respect to time. We find that the system order has an important influence on the running state of the system. The system has a periodic motion when the order meets the conditions of Hopf bifurcation; the fractional-order system gradually stabilizes with the change of the order and parameters while the corresponding integer-order system diverges. This study has certain significance to policy-making about macroeconomic regulation and control.

Adaptive Synchronization of a Stochastic Fractional-Order System

2015 ◽  
Vol 733 ◽  
pp. 939-942
Author(s):  
Xiao Jun Liu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Stochastic System ◽  
Fractional Order System ◽  
Adaptive Synchronization ◽  
Order System ◽  
Unknown Parameters ◽  
Adaptive Laws

In this paper, adaptive synchronization of a stochastic fractional-order system with unknown parameters is studied. Firstly, the stochastic system is reduced into the equivalent deterministic one with Laguerre approximation. Then, the synchronization for the system is realized by designing appropriate controllers and adaptive laws of the unknown parameters. Numerical simulations are carried out to demonstrate the effectiveness of the controllers and laws.

scholarly journals Fractional-order iterative learning control for singular fractional- order system: (P) - PDa type

2016 ◽  
Vol 66 (3) ◽  
pp. 40-49 ◽  
Author(s):  
Mihailo Lazarevic ◽  
Nikola Djurovic ◽  
Bosko Cvetkovic ◽  
Petar Mandic ◽  
Ljubisa Bucanovic
Keyword(s):  
Fractional Order ◽  
Iterative Learning Control ◽  
Learning Control ◽  
Iterative Learning ◽  
Fractional Order System ◽  
Order System ◽  
System P
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