TITLE

Bifurcation in the stable manifold of the bioreactor with nth and mth order polynomial yields

AUTHOR(S)
Xuncheng Huang; Lemin Zhu
PUB. DATE
July 2009
SOURCE
Journal of Mathematical Chemistry;Jul2009, Vol. 46 Issue 1, p199
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The three dimensional chemostat with nth and mth order polynomial yields, instead of the particular one such as A + BS, A + BS2, A + BS3, A + BS4, A + BS2 + CS3 and A + BS n, is proposed. The existence of limit cycles in the two-dimensional stable manifold, the Hopf bifurcation and the stability of the periodic solution created by the bifurcation are proved.
ACCESSION #
37308780

 

Related Articles

  • A polycycle and limit cycles in a non-differentiable predator-prey model. Sáez, E.; Szánto, I. // Proceedings of the Indian Academy of Sciences: Mathematical Scie;May2007, Vol. 117 Issue 2, p219 

    For a non-differentiable predator-prey model, we establish conditions for the existence of a heteroclinic orbit which is part of one contractive polycycle and for some values of the parameters, we prove that the heteroclinic orbit is broken and generates a stable limit cycle. In addition, in the...

  • GLOBAL HOPF BRANCHES IN A DELAYED MODEL FOR IMMUNE RESPONSE TO HTLV-1 INFECTIONS: COEXISTENCE OF MULTIPLE LIMIT CYCLES. LI, MICHAEL Y.; LIN, XIHUI; WANG, HAO // Canadian Applied Mathematics Quarterly;Spring2012, Vol. 20 Issue 1, p39 

    For an HTLV-I infection model, Li and Shu has shown in [6] that delayed CTL response can lead to com-plex bifurcations, and in particular, coexistence of multiple sta-ble periodic solutions. In this paper, we extend results of Li and Shu in [6] and investigate the case when there exist three...

  • AN AGE-STRUCTURED MODEL OF CANNIBALISM. Mařík, Robert; Přibylová, Lenka // Electronic Journal of Differential Equations;2006, Vol. 2006, Special section p1 

    We investigate the predator-prey model with cannibalism in the predator population, suggested by Magnusson [5] in 1995. We explore the model by a theory of bifurcations, based mainly on the results of Bautin. Among others, we show that the limit cycle appearing in the model due to the...

  • Interactions between oscillatory modes near a 2:3 resonant Hopf-Hopf bifurcation. Revel, G.; Alonso, D. M.; Moiola, J. L. // Chaos;Dec2010, Vol. 20 Issue 4, p043106 

    In this paper, the dynamics near a 2:3 resonant Hopf-Hopf bifurcation is studied. The main result is the identification of a distinctive structure connecting 1:2 and 1:3 strong resonances of limit cycles. This structure is found near the Hopf-Hopf point revealing that it may be associated to the...

  • Bifurcation Analysis of a Chemostat Model of Plasmid-Bearing and Plasmid-Free Competition with Pulsed Input. Zhong Zhao; Baozhen Wang; Liuyong Pang; Ying Chen // Journal of Applied Mathematics;2014, p1 

    A chemostat model of plasmid-bearing and plasmid-free competition with pulsed input is proposed. The invasion threshold of the plasmid-bearing and plasmid-free organisms is obtained according to the stability of the boundary periodic solution. By use of standard techniques of bifurcation theory,...

  • Mechanism and model of the oscillatory electro-oxidation of methanol. Sauerbrei, S.; Nascimento, M. A.; Eiswirth, M.; Varela, H. // Journal of Chemical Physics;4/21/2010, Vol. 132 Issue 15, p154901 

    A mechanism for the kinetic instabilities observed in the galvanostatic electro-oxidation of methanol is suggested and a model developed. The model is investigated using stoichiometric network analysis as well as concepts from algebraic geometry (polynomial rings and ideal theory) revealing the...

  • EVALUATING CYCLICITY OF CUBIC SYSTEMS WITH ALGORITHMS OF COMPUTATIONAL ALGEBRA. Levandovskyy, Viktor; Pfister, Gerhard; Romanovski, Valery G. // Communications on Pure & Applied Analysis;Sep2012, Vol. 11 Issue 5, p2029 

    We describe an algorithmic approach to studying limit cycle bifurcations in a neighborhood of an elementary center or focus of a polynomial system. Using it we obtain an upper bound for cyclicity of a family of cubic systems. Then using a theorem by Christopher [3] we study bifurcation of limit...

  • Dulac-Cherkas function in a neighborhood of a structurally unstable focus of an autonomous polynomial system on the plane. Grin', A. // Differential Equations;Jan2014, Vol. 50 Issue 1, p1 

    We consider the problem of estimating the number of limit cycles and their localization for an autonomous polynomial system on the plane with fixed real coefficients and with a small parameter. At the origin, the system has a structurally unstable focus whose first Lyapunov focal quantity is...

  • The Number of Limit Cycles of a Polynomial System on the Plane. Chao Liu; Maoan Han // Abstract & Applied Analysis;2013, p1 

    We perturb the vector field x = -yC(x, y), y = xC(X, Y) with a polynomial perturbation of degree n, where C(x, y) = (1 - y2)m, and study the number of limit cycles bifurcating from the period annulus surrounding the origin.

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics