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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

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 modi ed 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

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 modi ed 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 Articles
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

Publication Date April 1, 2016
Submission Date July 10, 2014
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Weı, H.-c., Lın, J.-t., Hwang, S.-f., Chen, Y.-y. (2016). ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp Journal of Mathematics, 4(1), 185-192.
AMA Weı Hc, Lın Jt, Hwang Sf, Chen Yy. ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp J. Math. April 2016;4(1):185-192.
Chicago Weı, Hsiu-chuan, Jenn-tsann Lın, Shin-feng Hwang, and Yuh-yih Chen. “ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES”. Konuralp Journal of Mathematics 4, no. 1 (April 2016): 185-92.
EndNote Weı H-c, Lın J-t, Hwang S-f, Chen Y-y (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 H.-c. Weı, J.-t. Lın, S.-f. Hwang, and Y.-y. 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, 2016.
ISNAD Weı, Hsiu-chuan et al. “ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES”. Konuralp Journal of Mathematics 4/1 (April 2016), 185-192.
JAMA Weı H-c, Lın J-t, Hwang S-f, Chen Y-y. 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, 2016, pp. 185-92.
Vancouver Weı H-c, Lın J-t, Hwang S-f, Chen Y-y. ON THE CODIMENSION-TWO AND -THREE BIFURCATIONS OF A FOOD WEB OF FOUR SPECIES. Konuralp J. Math. 2016;4(1):185-92.
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