Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

A Liapunov function for four-dimensional positive feedback systems


Author: Ji Fa Jiang
Journal: Quart. Appl. Math. 52 (1994), 601-614
MSC: Primary 34C11; Secondary 92C40
DOI: https://doi.org/10.1090/qam/1306039
MathSciNet review: MR1306039
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we use elementary symmetric polynomials in parameters to construct a Liapunov function for four-dimensional positive feedback systems. By applying it, we give a sufficient condition for every positive-time trajectory to converge to an equilibrium.


References [Enhancements On Off] (What's this?)

  • [1] J. F. Selgrade, Mathematical analysis of a cellular control process with positive feedback, SIAM J. Appl. Math. 36, 219-229 (1979)
  • [2] J. F. Selgrade, Asymptotic behavior of solutions to single loop positive feedback systems, J. Differential Equations 38, 80-103 (1980)
  • [3] J. F. Selgrade, A Hopf bifurcation in single-loop positive feedback systems, Quart. Appl. Math. 40, 347-351 (1982)
  • [4] M. W. Hirsch, Systems of differential equations that are competitive or cooperative. II: Convergence almost everywhere, SIAM J. Math. Anal. 16, 423-439 (1985)
  • [5] M. W. Hirsch, Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems, J. Differential Equations 80, 94-106 (1989)
  • [6] J. S. Griffith, Mathematics of cellular control processes. II: Positive feedback to one gene, J. Theoret. Biol. 20, 209-216 (1968)
  • [7] J. J. Tyson and H. G. Othmer, The dynamics of feedback control circuits in biochemical pathways, Progr. Theoret. Biol. 5, 1-62 (1978)
  • [8] J. P. LaSalle, Stability theory for ordinary differential equations, J. Differential Equations 4, 57-65 (1968)
  • [9] Jiang Ji-Fa, A Liapunov function for 3-dimensional feedback systems, Proc. Amer. Math. Soc. 114, 1009-1013 (1992)
  • [10] Jiang Ji-Fa, The asymptotic behavior of a class of second order differential equations with applications to electrical circuit equations, J. Math. Anal. Appl. 149, 26-37 (1990)
  • [11] Jiang Ji-Fa, On the asymptotic behavior of a class of nonlinear differential equations, Nonlinear Anal. TMA 14, 453-467 (1990)
  • [12] Jiang Ji-Fa, A note on a global stability theorem of M. W. Hirsch, Proc. Amer. Math. Soc. 112, 803-806 (1991)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34C11, 92C40

Retrieve articles in all journals with MSC: 34C11, 92C40


Additional Information

DOI: https://doi.org/10.1090/qam/1306039
Article copyright: © Copyright 1994 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website