Globally asymptotically stable analysis in a discrete time eco-epidemiological system

Zengyun Hu; Zhidong Teng; Tailei Zhang; Qiming Zhou; Xi Chen

doi:10.1016/j.chaos.2017.03.042

Globally asymptotically stable analysis in a discrete time eco-epidemiological system

Zengyun Hu, Zhidong Teng, Tailei Zhang, Qiming Zhou, Xi Chen^*

^*Corresponding author for this work

Department of Geography

Research output: Contribution to journal › Journal article › peer-review

11 Citations (Scopus)

Abstract

In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

Original language	English
Pages (from-to)	20-31
Number of pages	12
Journal	Chaos, Solitons and Fractals
Volume	99
DOIs	https://doi.org/10.1016/j.chaos.2017.03.042
Publication status	Published - Jun 2017

Scopus Subject Areas

Statistical and Nonlinear Physics
Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

User-Defined Keywords

Chaos
Discrete eco-epidemiological system
Flip bifurcation
Globally asymptotically stable
Hopf bifurcation
Predator-prey

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10.1016/j.chaos.2017.03.042

Cite this

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title = "Globally asymptotically stable analysis in a discrete time eco-epidemiological system",

abstract = "In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.",

keywords = "Chaos, Discrete eco-epidemiological system, Flip bifurcation, Globally asymptotically stable, Hopf bifurcation, Predator-prey",

author = "Zengyun Hu and Zhidong Teng and Tailei Zhang and Qiming Zhou and Xi Chen",

note = "Funding information: Supported National Natural Science Foundation of P.R. China [11401569, 11361059], Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 16JK1331), Hong Kong Research Grants Council (RGC) General Research Fund (GRF) (HKBU 203913), Hong Kong Baptist University Faculty Research Grant (FRG2/14-15/073), and Hong Kong Scholars Program. Publisher copyright: {\textcopyright} 2017 Elsevier Ltd. All rights reserved.",

year = "2017",

month = jun,

doi = "10.1016/j.chaos.2017.03.042",

language = "English",

volume = "99",

pages = "20--31",

journal = "Chaos, Solitons and Fractals",

issn = "0960-0779",

publisher = "Elsevier Ltd.",

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TY - JOUR

T1 - Globally asymptotically stable analysis in a discrete time eco-epidemiological system

AU - Hu, Zengyun

AU - Teng, Zhidong

AU - Zhang, Tailei

AU - Zhou, Qiming

AU - Chen, Xi

N1 - Funding information: Supported National Natural Science Foundation of P.R. China [11401569, 11361059], Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No. 16JK1331), Hong Kong Research Grants Council (RGC) General Research Fund (GRF) (HKBU 203913), Hong Kong Baptist University Faculty Research Grant (FRG2/14-15/073), and Hong Kong Scholars Program. Publisher copyright: © 2017 Elsevier Ltd. All rights reserved.

PY - 2017/6

Y1 - 2017/6

N2 - In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

AB - In this study, the dynamical behaviors of a discrete time eco-epidemiological system are discussed. The local stability, bifurcation and chaos are obtained. Moreover, the global asymptotical stability of this system is explored by an iteration scheme. The numerical simulations illustrate the theoretical results and exhibit the complex dynamical behaviors such as flip bifurcation, Hopf bifurcation and chaotic dynamical behaviors. Our main results provide an efficient method to analyze the global asymptotical stability for general three dimensional discrete systems.

KW - Chaos

KW - Discrete eco-epidemiological system

KW - Flip bifurcation

KW - Globally asymptotically stable

KW - Hopf bifurcation

KW - Predator-prey

UR - http://www.scopus.com/inward/record.url?scp=85016072608&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2017.03.042

DO - 10.1016/j.chaos.2017.03.042

M3 - Journal article

AN - SCOPUS:85016072608

SN - 0960-0779

VL - 99

SP - 20

EP - 31

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

ER -

Globally asymptotically stable analysis in a discrete time eco-epidemiological system

Abstract

Scopus Subject Areas

User-Defined Keywords

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