Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models

Wang, Yufeng; Qian, Youhua; Lin, Bingwen

doi:10.1155/2020/1351397

Cited by 3 publications

(2 citation statements)

References 22 publications

(29 reference statements)

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“…In 2019, Wang et al [32] proved the existence and uniqueness of relaxation oscillations of system (3) using knowledge of geometric singular perturbation theory. In 2020, Wang et al [33] introduced time delay on the basis of system (3), and obtained:…”

Section: Introductionmentioning

confidence: 99%

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Dynamic behavior of a class of predator-prey model with two time delays

Peng

Ren

Qian

2022

Preprint

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In this paper, three modified Lesile-Gower predator-prey models with two time delays are considered. Taking the time delay as bifurcation parameter, when Hopf bifurcation occurs, the critical value corresponding to time delay is obtained. By using normal form theory and central manifold argument, the direction of Hopf bifurcation and the stability of bifurcation periodic solution can be determined. Finally, numerical simulation is performed to support theoretical analysis.

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Section: Introductionmentioning

confidence: 99%

“…Wang [33] adopted Taylor expansion for the time delay term, and studied the influence of time delay on its dynamic characteristics by using geometric singular perturbation theory. However, the error of Taylor expansion is relatively large and the result is not accurate enough.…”

Section: Introductionmentioning

confidence: 99%

Dynamic behavior of a class of predator-prey model with two time delays

Peng

Ren

Qian

2022

Preprint

Self Cite

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Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate

Zhang,

Wang,

Cai

2024

Complexity

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The periodic oscillation transmission of infectious diseases is widespread, deep understanding of this periodic pattern and exploring the generation mechanism, and identifying the specific factors that lead to such periodic outbreaks, which are of very importanceto predict and control the spread of infectious diseases. In this study, to further reveal the mathematical mechanism of spontaneous generation of periodic oscillation solution, we investigate a type of SEIR epidemic model with a small intrinsic growth rate. By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three‐dimensional SIR models to the four‐dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. Numerical simulations are performed to verify our theoretical results. The results presented in this study provide a new idea for the study of the intrinsic mechanism of periodic oscillation in epidemiology, enrich the dynamics of epidemic models, and deepen the understanding of the global dynamics of these models.

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Relaxation Oscillations and Dynamical Properties in a Time Delay Slow–Fast Predator–Prey Model with a Piecewise Smooth Functional Response

et al. 2022

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In the past few decades, the predator–prey model has played an important role in the dynamic behavior of populations. Many scholars have studied the stability of the predator–prey system. Due to the complex influence of time delay on the dynamic behavior of systems, time-delay systems have garnered wide interest. In this paper, a classical piecewise smooth slow–fast predator–prey model is considered. The dynamic properties of the system are analyzed by linearization. The existence and uniqueness of the relaxation oscillation are then proven through the geometric singular perturbation theory and entry–exit function. Finally, a stable limit cycle is obtained. A numerical simulation verifies our results for the systems and shows the effectiveness of the method in dealing with time delays.

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Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models

Cited by 3 publications

References 22 publications

Dynamic behavior of a class of predator-prey model with two time delays

Dynamic behavior of a class of predator-prey model with two time delays

Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate

Relaxation Oscillations and Dynamical Properties in a Time Delay Slow–Fast Predator–Prey Model with a Piecewise Smooth Functional Response

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