Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays

Zhang, Jiangang; Lu, Jiarong; Du, Wenju; Chu, Yan-Dong; Luo, Hongwei

doi:10.22436/jnsa.010.08.14

Cited by 3 publications

(2 citation statements)

References 17 publications

(19 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Author details 1 College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan, 030006, China. 2 Institute of Mathematical Physics, Technische Universität Berlin, Berlin, D-10587, Germany.…”

Section: Publisher's Notementioning

confidence: 99%

See 1 more Smart Citation

Retraction Note: New applications of Schrödinger type inequalities to the existence and uniqueness of Schrödingerean equilibrium

Wang

Roncalver

2021

J Inequal Appl

View full text Add to dashboard Cite

Section: Publisher's Notementioning

confidence: 99%

“…

The Editors-in-Chief have retracted this article because it shows significant overlap with articles by different authors that were simultaneously under consideration at different journals [1,2]. The article also shows evidence of authorship manipulation and peer review manipulation.

…”

mentioning

confidence: 99%

Retraction Note: New applications of Schrödinger type inequalities to the existence and uniqueness of Schrödingerean equilibrium

Wang

Roncalver

2021

J Inequal Appl

View full text Add to dashboard Cite

Hopf bifurcation of the model with terms of two time-delays and delay-dependent parameter based on the theory of crossing curves

Dong

Liu

et al. 2022

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

A three-layer prey–predator model with two time-delays and one delay-dependent parameter is established in this paper. To begin, the paper calculates the conditions for each population in the model to maintain the quantity stable and Hopf bifurcation when [Formula: see text], [Formula: see text], [Formula: see text] is in the stable interval, and [Formula: see text]. The crossing curves, their type, and the direction of the crossing curves are then obtained using the crossing curve method, which is composed of the threshold values of the dynamic behavior change on the two time-delays plane when [Formula: see text]. The real data from the forage grass– Ochotona curzoniae–Buteo hemilasius food chain is used to conduct an empirical study of the model. When [Formula: see text], the feasible region of the crossing curves is open-ended, and the model's crossing curves on the [Formula: see text] plane are truncated. This indicates that the model's threshold distribution of dynamic behavior change is a regular curve made of several curves. The simulation using the time-delay value on the crossing curves shows that the model produces different dynamic behaviors such as stability, bifurcation, and chaos depending on the time-delay value on both sides of the curves. The critical values of dynamic behavior change are time-delay values on the crossing curves. The empirical study shows that increasing Ochotona curzoniae’s environmental capacity can easily cause Hopf bifurcation of the system. At this time, the number of each population in the Plateau ecosystem constantly fluctuates, and Ochotona curzoniae is vulnerable to extinction.

show abstract

Retraction Note to: Stability and direction for a class of Schrödingerean difference equations with delay

Lai

Sun

Li³

2020

Adv Differ Equ

View full text Add to dashboard Cite

show abstract

Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays

Cited by 3 publications

References 17 publications

Retraction Note: New applications of Schrödinger type inequalities to the existence and uniqueness of Schrödingerean equilibrium

Retraction Note: New applications of Schrödinger type inequalities to the existence and uniqueness of Schrödingerean equilibrium

Hopf bifurcation of the model with terms of two time-delays and delay-dependent parameter based on the theory of crossing curves

Retraction Note to: Stability and direction for a class of Schrödingerean difference equations with delay

Contact Info

Product

Resources

About