ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES

Hsiu-chuan Weı; Jenn-tsann Lın; Shin-feng Hwang; Yuh-yih Chen

Research Article

ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES

Year 2016, Volume: 4 Issue: 1, 185 - 192, 01.04.2016

Hsiu-chuan Weı Jenn-tsann Lın Shin-feng Hwang Yuh-yih Chen

https://izlik.org/JA79DW55ZM

Abstract

This paper is concerned with codimension-two and -three bifurca- tions of a food web containing a bottom prey X, two competing predators Y and Z on X, and a super predator W only on Y . Parameter conditions for a part of codimension-two bifurcations and a codimension-three bifurcation are derived. Three-parameter bifurcation diagrams are computed using an adap- tive grid method to locate the bifurcations determined by the eigenvalues of equilibria.

Keywords

food web; bifurcation; numerical computation.

References

[1] B. Deng, Food chain chaos due to junction-fold point, Chaos Vol:11, (2001), 514-525.
[2] B. Deng and G. Hines, Food chain chaos due to Shilnikov's orbit, Chaos Vol:12, (2002), 533-538.
[3] B. Deng and G. Hines, Food chain chaos due to transcritical point, Chaos Vol:13, (2003), 578-585.
[4] B. Deng, Food chain chaos with canard explosion, Chaos Vol:14, (2004), 1083-1092.
[5] B. Bockelman, B. Deng, E. Green, G. Hines, L. Lippitt, and J. Sherman, Chaotic coexistence in a top-predator mediated competitive exclusive web, J. Dynam. Di. Eqns. Vol:16, No.4 (2004), 1061-1092.
[6] B. Bockelman and B. Deng, Food web chaos without subchain oscillators, Int. J. Bifurcation and Chaos Vol:15, No.11 (2005), 3481-3492.
[7] H.C. Wei, On the bifurcation analysis of a food web of four species, Appli. Math. Comput. Vol:215, No.9 (2010), 3280-3292.
[8] Z. Wei and L. Li, Hopf bifurcation analysis of a food web of four species, Int. J. Phys. Sci. Vol:7, No.2 (2012), 250-255.
[9] H.C. Wei, Numerical revisit to a class of one-predator, two-prey models, Int. J. Bifurcation Chaos Vol:20, No.8 (2010), 2521-2536.
[10] H.C. Wei, A modied numerical method for bifurcations of xed points of ODE systems with periodically pulsed inputs, Appli. Math. Comput. Vol:236 (2014), 373-383.

Year 2016, Volume: 4 Issue: 1, 185 - 192, 01.04.2016

Hsiu-chuan Weı Jenn-tsann Lın Shin-feng Hwang Yuh-yih Chen

https://izlik.org/JA79DW55ZM

Abstract

References

[1] B. Deng, Food chain chaos due to junction-fold point, Chaos Vol:11, (2001), 514-525.
[2] B. Deng and G. Hines, Food chain chaos due to Shilnikov's orbit, Chaos Vol:12, (2002), 533-538.
[3] B. Deng and G. Hines, Food chain chaos due to transcritical point, Chaos Vol:13, (2003), 578-585.
[4] B. Deng, Food chain chaos with canard explosion, Chaos Vol:14, (2004), 1083-1092.
[5] B. Bockelman, B. Deng, E. Green, G. Hines, L. Lippitt, and J. Sherman, Chaotic coexistence in a top-predator mediated competitive exclusive web, J. Dynam. Di. Eqns. Vol:16, No.4 (2004), 1061-1092.
[6] B. Bockelman and B. Deng, Food web chaos without subchain oscillators, Int. J. Bifurcation and Chaos Vol:15, No.11 (2005), 3481-3492.
[7] H.C. Wei, On the bifurcation analysis of a food web of four species, Appli. Math. Comput. Vol:215, No.9 (2010), 3280-3292.
[8] Z. Wei and L. Li, Hopf bifurcation analysis of a food web of four species, Int. J. Phys. Sci. Vol:7, No.2 (2012), 250-255.
[9] H.C. Wei, Numerical revisit to a class of one-predator, two-prey models, Int. J. Bifurcation Chaos Vol:20, No.8 (2010), 2521-2536.
[10] H.C. Wei, A modied numerical method for bifurcations of xed points of ODE systems with periodically pulsed inputs, Appli. Math. Comput. Vol:236 (2014), 373-383.

There are 10 citations in total.

Details

Primary Language	English
Subjects	Engineering
Journal Section	Research Article
Authors	Hsiu-chuan Weı This is me Jenn-tsann Lın This is me Shin-feng Hwang This is me Yuh-yih Chen This is me
Submission Date	July 10, 2014
Publication Date	April 1, 2016
IZ	https://izlik.org/JA79DW55ZM
Published in Issue	Year 2016 Volume: 4 Issue: 1

Cite

APA	Weı, H.- chuan, Lın, J.- tsann, Hwang, S.- feng, & Chen, Y.- yih. (2016). ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp Journal of Mathematics, 4(1), 185-192. https://izlik.org/JA79DW55ZM
AMA	1.Weı H chuan, Lın J tsann, Hwang S feng, Chen Y yih. ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp J. Math. 2016;4(1):185-192. https://izlik.org/JA79DW55ZM
Chicago	Weı, Hsiu-chuan, Jenn-tsann Lın, Shin-feng Hwang, and Yuh-yih Chen. 2016. “ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES”. Konuralp Journal of Mathematics 4 (1): 185-92. https://izlik.org/JA79DW55ZM.
EndNote	Weı H- chuan, Lın J- tsann, Hwang S- feng, Chen Y- yih (April 1, 2016) ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp Journal of Mathematics 4 1 185–192.
IEEE	[1]H.- chuan Weı, J.- tsann Lın, S.- feng Hwang, and Y.- yih Chen, “ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES”, Konuralp J. Math., vol. 4, no. 1, pp. 185–192, Apr. 2016, [Online]. Available: https://izlik.org/JA79DW55ZM
ISNAD	Weı, Hsiu-chuan - Lın, Jenn-tsann - Hwang, Shin-feng - Chen, Yuh-yih. “ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES”. Konuralp Journal of Mathematics 4/1 (April 1, 2016): 185-192. https://izlik.org/JA79DW55ZM.
JAMA	1.Weı H- chuan, Lın J- tsann, Hwang S- feng, Chen Y- yih. ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp J. Math. 2016;4:185–192.
MLA	Weı, Hsiu-chuan, et al. “ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES”. Konuralp Journal of Mathematics, vol. 4, no. 1, Apr. 2016, pp. 185-92, https://izlik.org/JA79DW55ZM.
Vancouver	1.Hsiu-chuan Weı, Jenn-tsann Lın, Shin-feng Hwang, Yuh-yih Chen. ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp J. Math. [Internet]. 2016 Apr. 1;4(1):185-92. Available from: https://izlik.org/JA79DW55ZM