Global Stability of a Non-Smooth Predator–Prey System with Holling I Functional Response and Refuge Effect

Yuan Tian; Hai Ting Sun; Yu Xia He

doi:10.4028/www.scientific.net/AMM.595.283

Paper Titles

A Novel Wireless Thermal Convection Type Inclinometer by Using Non-Floating Structure
p.243

Application of Taguchi Method in the Optimization of Antioxidant Activity for Australian Tea Tree
p.253

Comparison of Efficacy and Safety of Aripiprazole and Risperidone in the Treatment of Behavioral and Psychological Symptoms of Dementia
p.258

Predictive Models for Pre-Operative Diagnosis of Rotator Cuff Tear: A Comparison Study of Two Methods between Logistic Regression and Artificial Neural Network
p.263

Alpha Wave Attention EEG Analysis Based on the Multiscale Jensen-Shannon Divergence
p.269

Continuously Harvesting of a Phytoplankton-Zooplankton System with Holling I Functional Response
p.277

Global Stability of a Non-Smooth Predator–Prey System with Holling I Functional Response and Refuge Effect
p.283

Robust Edge Detection Based on Anisotropic Mathematical Morphology and Scale Multiplication in NSCT Domain
p.289

Coupling Analysis of Beta Rhythm Electroencephalogram Based on the Multiscale Mutual Mode Entropy
p.295

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 595Global Stability of a Non-Smooth Predator–Prey...

Global Stability of a Non-Smooth Predator–Prey System with Holling I Functional Response and Refuge Effect

Abstract:

This paper analyses the dynamics of a non-smooth predator-prey model with refuge effect, where the functional response is taken as Holling I type. To begin with, some preliminaries and the existence of regular, virtual, pseudo-equilibrium and tangent point are established. Then, the stability of trivial equilibrium and predator free equilibrium is discussed. Furthermore, it is shown that the regular equilibrium and the pseudo-equilibrium cannot coexist. Finally, the conclusion is given.

You might also be interested in these eBooks

Recent Engineering Decisions in Industry

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 595)

Pages:

283-288

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.595.283

Citation:

Cite this paper

Online since:

July 2014

Authors:

Yuan Tian*, Hai Ting Sun, Yu Xia He

Keywords:

Fillippov System, Global Stability, Holling i Functional Response, Predator-Prey, Refuge

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] Saez, E., Gonzalez-Olivares, E.: Dynamics of A Predator-Prey Model. SIAM J. Appl. Math. 59 (1999), 1867–1878.

DOI: 10.1137/s0036139997318457

Google Scholar

[2] B. Sahoo, A predator–prey model with general Holling interactions in presence of additional food, Int. J. Plant Res. 2 (2012) 47–50.

DOI: 10.5923/j.plant.20120201.07

Google Scholar

[3] S. Tang, J. Liang, Global qualitative analysis of a non-smooth Gause predator–prey model with a refuge, Nonlinear Anal. TMA 76 (2013) 165–180.

DOI: 10.1016/j.na.2012.08.013

Google Scholar

[4] B. Liu, Z. Teng, L. Chen, Analysis of a predator-prey model with Holling II functional response concerning impulsive control strategy, J. Comput. Appl. Math. 193 (2006) 347-362.

DOI: 10.1016/j.cam.2005.06.023

Google Scholar

[5] W. Wang, J. Shen, J.J. Nieto, Permanence and periodic solution of predatorprey system with Holling type functional response and impulses, Discrete Dyn. Nat. Soc. (2007) doi: 10. 1155/2007/81756.

DOI: 10.1155/2007/81756

Google Scholar

[6] A.F. Filippov, Differential Equations with Discontinuous Righthand Sides, Kluwer Academic, Dordrecht, (1988).

Google Scholar

[7] V.I. Utkin, J. Guldner, J.X. Shi, Sliding Mode Control in Electro-Mechanical Systems, second ed., Taylor and Francis Group, (2009).

DOI: 10.1201/9781420065619

Google Scholar