Monotone systems under positive feedback: multistability and a reduction theorem. Enciso, G. & Sontag, E. Systems Control Lett., 54(2):159–168, 2005. abstract bibtex For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a previous paper provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a consequence of the technique. The present paper extends the approach to multiple inputs and outputs. A key idea is the introduction of a reduced system which preserves local stability properties. New results characterizing strong monotonicity of feedback loops involving cascades are also presented.
@ARTICLE{enciso_sontagSCL05,
AUTHOR = {G.A. Enciso and E.D. Sontag},
JOURNAL = {Systems Control Lett.},
TITLE = {Monotone systems under positive feedback: multistability
and a reduction theorem},
YEAR = {2005},
OPTMONTH = {},
OPTNOTE = {},
NUMBER = {2},
PAGES = {159--168},
VOLUME = {54},
KEYWORDS = {multistability, systems biology, biochemical networks,
nonlinear stability, dynamical systems, monotone systems},
PDF = {../../FTPDIR/enciso_sontag_multistability_SCL04_inpress.pdf},
ABSTRACT = { For feedback loops involving single input, single
output monotone systems with well-defined I/O characteristics, a
previous paper provided an approach to determining the location and
stability of steady states. A result on global convergence for
multistable systems followed as a consequence of the technique. The
present paper extends the approach to multiple inputs and outputs. A
key idea is the introduction of a reduced system which preserves
local stability properties. New results characterizing strong
monotonicity of feedback loops involving cascades are also presented. }
}
Downloads: 0
{"_id":"DmRGwA5JEmfPBYAxD","bibbaseid":"enciso-sontag-monotonesystemsunderpositivefeedbackmultistabilityandareductiontheorem-2005","downloads":0,"creationDate":"2018-10-18T05:07:06.202Z","title":"Monotone systems under positive feedback: multistability and a reduction theorem","author_short":["Enciso, G.","Sontag, E."],"year":2005,"bibtype":"article","biburl":"http://www.sontaglab.org/PUBDIR/Biblio/complete-bibliography.bib","bibdata":{"bibtype":"article","type":"article","author":[{"firstnames":["G.A."],"propositions":[],"lastnames":["Enciso"],"suffixes":[]},{"firstnames":["E.D."],"propositions":[],"lastnames":["Sontag"],"suffixes":[]}],"journal":"Systems Control Lett.","title":"Monotone systems under positive feedback: multistability and a reduction theorem","year":"2005","optmonth":"","optnote":"","number":"2","pages":"159–168","volume":"54","keywords":"multistability, systems biology, biochemical networks, nonlinear stability, dynamical systems, monotone systems","pdf":"../../FTPDIR/enciso_sontag_multistability_SCL04_inpress.pdf","abstract":"For feedback loops involving single input, single output monotone systems with well-defined I/O characteristics, a previous paper provided an approach to determining the location and stability of steady states. A result on global convergence for multistable systems followed as a consequence of the technique. The present paper extends the approach to multiple inputs and outputs. A key idea is the introduction of a reduced system which preserves local stability properties. New results characterizing strong monotonicity of feedback loops involving cascades are also presented. ","bibtex":"@ARTICLE{enciso_sontagSCL05,\n AUTHOR = {G.A. Enciso and E.D. Sontag},\n JOURNAL = {Systems Control Lett.},\n TITLE = {Monotone systems under positive feedback: multistability \n and a reduction theorem},\n YEAR = {2005},\n OPTMONTH = {},\n OPTNOTE = {},\n NUMBER = {2},\n PAGES = {159--168},\n VOLUME = {54},\n KEYWORDS = {multistability, systems biology, biochemical networks, \n nonlinear stability, dynamical systems, monotone systems},\n PDF = {../../FTPDIR/enciso_sontag_multistability_SCL04_inpress.pdf},\n ABSTRACT = { For feedback loops involving single input, single \n output monotone systems with well-defined I/O characteristics, a \n previous paper provided an approach to determining the location and \n stability of steady states. A result on global convergence for \n multistable systems followed as a consequence of the technique. The \n present paper extends the approach to multiple inputs and outputs. A \n key idea is the introduction of a reduced system which preserves \n local stability properties. New results characterizing strong \n monotonicity of feedback loops involving cascades are also presented. }\n}\n\n","author_short":["Enciso, G.","Sontag, E."],"key":"enciso_sontagSCL05","id":"enciso_sontagSCL05","bibbaseid":"enciso-sontag-monotonesystemsunderpositivefeedbackmultistabilityandareductiontheorem-2005","role":"author","urls":{},"keyword":["multistability","systems biology","biochemical networks","nonlinear stability","dynamical systems","monotone systems"],"downloads":0,"html":""},"search_terms":["monotone","systems","under","positive","feedback","multistability","reduction","theorem","enciso","sontag"],"keywords":["multistability","systems biology","biochemical networks","nonlinear stability","dynamical systems","monotone systems"],"authorIDs":[],"dataSources":["DKqZbTmd7peqE4THw"]}