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

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

In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a c...

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Main Authors: Yufeng Wang, Youhua Qian, Bingwen Lin
Format: Article
Language:English
Published: Hindawi-Wiley 2020-01-01
Series:Complexity
Online Access:http://dx.doi.org/10.1155/2020/1351397
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spelling doaj-5d847e2425b14b84ab9cc4893cb2c8542020-11-25T03:05:29ZengHindawi-WileyComplexity1076-27871099-05262020-01-01202010.1155/2020/13513971351397Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower ModelsYufeng Wang0Youhua Qian1Bingwen Lin2College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaCollege of Mathematics and Computer Science, Zhejiang Normal University, Jinhua 321004, ChinaIn this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.http://dx.doi.org/10.1155/2020/1351397
collection DOAJ
language English
format Article
sources DOAJ
author Yufeng Wang
Youhua Qian
Bingwen Lin
spellingShingle Yufeng Wang
Youhua Qian
Bingwen Lin
Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models
Complexity
author_facet Yufeng Wang
Youhua Qian
Bingwen Lin
author_sort Yufeng Wang
title Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models
title_short Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models
title_full Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models
title_fullStr Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models
title_full_unstemmed Relaxation Oscillations and Dynamical Properties in Two Time-Delay Slow-Fast Modified Leslie-Gower Models
title_sort relaxation oscillations and dynamical properties in two time-delay slow-fast modified leslie-gower models
publisher Hindawi-Wiley
series Complexity
issn 1076-2787
1099-0526
publishDate 2020-01-01
description In this paper, we consider two kinds of time-delay slow-fast modified Leslie-Gower models. For the first system, we prove the existence and uniqueness of relaxation oscillation cycle through the geometric singular perturbation theory and entry-exit function. For the second system, we put forward a conjecture that the relaxation oscillation of the system is unique. Numerical simulation also verifies our results for the systems.
url http://dx.doi.org/10.1155/2020/1351397
work_keys_str_mv AT yufengwang relaxationoscillationsanddynamicalpropertiesintwotimedelayslowfastmodifiedlesliegowermodels
AT youhuaqian relaxationoscillationsanddynamicalpropertiesintwotimedelayslowfastmodifiedlesliegowermodels
AT bingwenlin relaxationoscillationsanddynamicalpropertiesintwotimedelayslowfastmodifiedlesliegowermodels
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