A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems

Eyal Weiss; Michael Margaliot

doi:10.1109/CDC.2018.8619509

A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems

Eyal Weiss, Michael Margaliot

Tel Aviv University

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Scopus citations

Abstract

Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology, ecology, and chemistry. Smith (1991) has extended Smillie's result and proved entrainment in the case where the vector field is time-varying and periodic. We use the theory of linear totally nonnegative differential systems developed by Schwarz (1970) to give a generalization of these two results. This is based on weakening the requirement for strong cooperativity to cooperativity, and adding an additional observability-type condition.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	3080-3085
Number of pages	6
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619509
State	Published - 2 Jul 2018
Externally published	Yes
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

Bibliographical note

Publisher Copyright:
© 2018 IEEE.

Funding

Research supported in part by research grants from the Israeli Ministry of Science and Technology, the Israel Science Foundation, and the US-Israel Binational Science Foundation.

Funders	Funder number
United States-Israel Binational Science Foundation
Israel Science Foundation
Ministry of science and technology, Israel

Access to Document

10.1109/CDC.2018.8619509

Cite this

Weiss, E., & Margaliot, M. (2018). A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 3080-3085). Article 8619509 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8619509

@inproceedings{4188426df94f449299f1c8117dcf9a75,

title = "A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems",

abstract = "Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology, ecology, and chemistry. Smith (1991) has extended Smillie's result and proved entrainment in the case where the vector field is time-varying and periodic. We use the theory of linear totally nonnegative differential systems developed by Schwarz (1970) to give a generalization of these two results. This is based on weakening the requirement for strong cooperativity to cooperativity, and adding an additional observability-type condition.",

author = "Eyal Weiss and Michael Margaliot",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

year = "2018",

month = jul,

day = "2",

doi = "10.1109/CDC.2018.8619509",

language = "אנגלית",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

pages = "3080--3085",

booktitle = "2018 IEEE Conference on Decision and Control, CDC 2018",

address = "ארצות הברית",

}

Weiss, E & Margaliot, M 2018, A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8619509, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 3080-3085, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8619509

A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems. / Weiss, Eyal; Margaliot, Michael.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 3080-3085 8619509 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems

AU - Weiss, Eyal

AU - Margaliot, Michael

PY - 2018/7/2

Y1 - 2018/7/2

N2 - Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology, ecology, and chemistry. Smith (1991) has extended Smillie's result and proved entrainment in the case where the vector field is time-varying and periodic. We use the theory of linear totally nonnegative differential systems developed by Schwarz (1970) to give a generalization of these two results. This is based on weakening the requirement for strong cooperativity to cooperativity, and adding an additional observability-type condition.

AB - Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology, ecology, and chemistry. Smith (1991) has extended Smillie's result and proved entrainment in the case where the vector field is time-varying and periodic. We use the theory of linear totally nonnegative differential systems developed by Schwarz (1970) to give a generalization of these two results. This is based on weakening the requirement for strong cooperativity to cooperativity, and adding an additional observability-type condition.

UR - http://www.scopus.com/inward/record.url?scp=85062184962&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619509

DO - 10.1109/CDC.2018.8619509

M3 - ???researchoutput.researchoutputtypes.contributiontobookanthology.conference???

AN - SCOPUS:85062184962

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 3080

EP - 3085

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

Y2 - 17 December 2018 through 19 December 2018

ER -

A Generalization of Smillie's Theorem on Strongly Cooperative Tridiagonal Systems

Abstract

Publication series

Conference

Bibliographical note

Funding

Access to Document

Other files and links

Fingerprint

Cite this