Bifurcation analysis and chaos control in a discrete‐time plant quality and larch budmoth interaction model with Ricker equation

2019 ◽  
Vol 42 (18) ◽  
pp. 7395-7410
Author(s):  
Irfan Ali ◽  
Umer Saeed ◽  
Qamar Din
Keyword(s):  
Discrete Time ◽  
Bifurcation Analysis ◽  
Chaos Control ◽  
Interaction Model ◽  
Plant Quality

scholarly journals Bifurcation analysis and chaos control in discrete-time modified Leslie–Gower prey harvesting model

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Muhammad Bilal Ajaz ◽  
Umer Saeed ◽  
Qamar Din ◽  
Irfan Ali ◽  
Muhammad Israr Siddiqui
Keyword(s):  
Discrete Time ◽  
Bifurcation Analysis ◽  
Chaos Control

Intervention Time in Target-Oriented Chaos Control

2021 ◽  
Vol 31 (09) ◽  
pp. 2150134
Author(s):  
Juan Segura
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Single Species ◽  
Positive Equilibrium ◽  
Population Stability ◽  
Determine Parameter ◽  
And Control ◽  
Parameter Values ◽  
Proportional Feedback

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

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