Detection of Hopf bifurcations induced by pregnancy and maturation delays in a spatial predator–prey model via crossing curves method

Li, Shuai; Huang, Chengdai; Song, Xinyu

doi:10.1016/j.chaos.2023.114012

Cited by 5 publications

(1 citation statement)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the viewpoint of mathematics, delay is a vital factor that affects the dynamical traits of various differential systems. In various cases, a delay will result in an alteration of stability, the emergence of bifurcation and the onset of chaos and so on [12]. One can also see [13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Behavior and Hybrid Controller Design of a 2D Lotka–Volterra Commensal Symbiosis System Accompanying Delay

Cui,

Xu,

et al. 2023

Mathematics

View full text Add to dashboard Cite

All the time, differential dynamical models with delay has witness a tremendous application value in characterizing the internal law among diverse biological populations in biology. In the current article, on the basis of the previous publications, we formulate a new Lotka–Volterra commensal symbiosis system accompanying delay. Utilizing fixed point theorem, inequality tactics and an appropriate function, we gain the sufficient criteria on existence and uniqueness, non-negativeness and boundedness of the solution to the formulated delayed Lotka–Volterra commensal symbiosis system. Making use of stability and bifurcation theory of delayed differential equation, we focus on the emergence of bifurcation behavior and stability nature of the formulated delayed Lotka–Volterra commensal symbiosis system. A new delay-independent stability and bifurcation conditions on the model are presented. By constructing a positive definite function, we explore the global stability. By constructing two diverse hybrid delayed feedback controllers, we can adjusted the domain of stability and time of appearance of Hopf bifurcation of the delayed Lotka–Volterra commensal symbiosis system. The effect of time delay on the domain of stability and time of appearance of Hopf bifurcation of the model is given. Matlab experiment diagrams are provided to sustain the acquired key outcomes.

show abstract