scholarly journals Hopf bifurcation and chaos control for a Leslie–Gower type generalist predator model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Qin Chen ◽  
Jianguo Gao
Keyword(s):  
Hopf Bifurcation ◽  
Chaos Control ◽  
Generalist Predator ◽  
Bifurcation And Chaos ◽  
Predator Model

Stability, bifurcation and chaos control of a discretized Leslie prey-predator model

2021 ◽  
Vol 152 ◽  
pp. 111345
Author(s):  
S. Akhtar ◽  
R. Ahmed ◽  
M. Batool ◽  
Nehad Ali Shah ◽  
Jae Dong Chung
Keyword(s):  
Chaos Control ◽  
Bifurcation And Chaos ◽  
Predator Model

Hopf bifurcation and chaos in a Leslie–Gower prey–predator model with discrete delays

2020 ◽  
Vol 13 (06) ◽  
pp. 2050048
Author(s):  
Anuraj Singh ◽  
Preeti ◽  
Pradeep Malik
Keyword(s):  
Periodic Solution ◽  
Hopf Bifurcation ◽  
Bifurcation And Chaos ◽  
Normal Form Theory ◽  
Periodic Oscillations ◽  
Discrete Delays ◽  
Form Theory ◽  
Delayed System ◽  
Predator Model ◽  
Boundedness And Persistence

In this work, a Leslie–Gower prey-predator model with two discrete delays has been investigated. The positivity, boundedness and persistence of the delayed system have been discussed. The system exhibits the phenomenon of Hopf bifurcation with respect to both delays. The conditions for occurrence of Hopf bifurcation are obtained for different combinations of delays. It is shown that delay induces the complexity in the system and brings the periodic oscillations, quasi-periodic oscillations and chaos. The properties of periodic solution have been determined using central manifold and normal form theory. Further, the global stability of the system has been established for different cases of discrete delays. The numerical computation has also been performed to verify analytical results.

Hopf bifurcation and chaos in macroeconomic models with policy lag

2005 ◽  
Vol 25 (1) ◽  
pp. 91-108 ◽  
Author(s):  
Xiaofeng Liao ◽  
Chuandong Li ◽  
Shangbo Zhou
Keyword(s):  
Hopf Bifurcation ◽  
Bifurcation And Chaos ◽  
Macroeconomic Models

scholarly journals Stability, bifurcation, and chaos control of a novel discrete-time model involving Allee effect and cannibalism

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Sajjad Shabbir ◽  
Qamar Din ◽  
Khalil Ahmad ◽  
Asifa Tassaddiq ◽  
Atif Hassan Soori ◽  
...  
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Allee Effect ◽  
Bifurcation And Chaos ◽  
Time Model ◽  
Discrete Time Model

scholarly journals Hopf Bifurcation and Chaos of a Delayed Finance System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Xuebing Zhang ◽  
Honglan Zhu
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Center Manifold ◽  
Chaotic State ◽  
Bifurcation And Chaos ◽  
Finance System ◽  
Center Manifold Theorem ◽  
Normal Form Method ◽  
Simulation Results ◽  
The Stability

In this paper, a finance system with delay is considered. By analyzing the corresponding characteristic equations, the local stability of equilibrium is established. The existence of Hopf bifurcations at the equilibrium is also discussed. Furthermore, formulas for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theorem. Finally, numerical simulation results are presented to validate the theoretical analysis. Numerical simulation results show that delay can lead a stable system into a chaotic state.

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