Stability of a certain 2-dimensional map with cobweb diagram

Sinan Kapçak

doi:10.1007/978-3-319-42085-1_4

Stability of a certain 2-dimensional map with cobweb diagram

Sinan Kapçak

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

3 Citations (Scopus)

Abstract

In this paper, we investigate the following discrete-time map: x_n+1 = φ(y_n), y_n+1 = ψ(x_n). We introduce a novel method to determine the stability of the given two-dimensional map by using a one-dimensional map. A cobweb-like diagram is also introduced in order to analyze the stability of the system. We show that the stability of a fixed point in cobweb diagram implies the stability in phase diagram for the given system. In addition, an application of the system to a non-hyperbolic fixed point is also given.

Original language	English
Title of host publication	Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings
Editors	Bernady O. Apduhan, Beniamino Murgante, Sanjay Misra, David Taniar, Carmelo M. Torre, Ana Maria A.C. Rocha, Shangguang Wang, Osvaldo Gervasi, Elena Stankova
Publisher	Springer
Pages	45-53
Number of pages	9
ISBN (Print)	9783319420844
DOIs	https://doi.org/10.1007/978-3-319-42085-1_4
Publication status	Published - 2016
Externally published	Yes
Event	16th International Conference on Computational Science and Its Applications, ICCSA 2016 - Beijing, China Duration: 4 Jul 2016 → 7 Jul 2016

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	9786
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	16th International Conference on Computational Science and Its Applications, ICCSA 2016
Country/Territory	China
City	Beijing
Period	4/07/16 → 7/07/16

Bibliographical note

Publisher Copyright:
© Springer International Publishing Switzerland 2016.

Keywords

Cobweb diagram
Discrete dynamical systems
Global stability
Isoclines
Root finding algorithm

Access to Document

10.1007/978-3-319-42085-1_4

Cite this

Kapçak, S. (2016). Stability of a certain 2-dimensional map with cobweb diagram. In B. O. Apduhan, B. Murgante, S. Misra, D. Taniar, C. M. Torre, A. M. A. C. Rocha, S. Wang, O. Gervasi, & E. Stankova (Eds.), Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings (pp. 45-53). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9786). Springer. https://doi.org/10.1007/978-3-319-42085-1_4

Kapçak, Sinan. / Stability of a certain 2-dimensional map with cobweb diagram. Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings. editor / Bernady O. Apduhan ; Beniamino Murgante ; Sanjay Misra ; David Taniar ; Carmelo M. Torre ; Ana Maria A.C. Rocha ; Shangguang Wang ; Osvaldo Gervasi ; Elena Stankova. Springer, 2016. pp. 45-53 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{913aa5dee6a5414cbdd7664ab850cf61,

title = "Stability of a certain 2-dimensional map with cobweb diagram",

abstract = "In this paper, we investigate the following discrete-time map: xn+1 = φ(yn), yn+1 = ψ(xn). We introduce a novel method to determine the stability of the given two-dimensional map by using a one-dimensional map. A cobweb-like diagram is also introduced in order to analyze the stability of the system. We show that the stability of a fixed point in cobweb diagram implies the stability in phase diagram for the given system. In addition, an application of the system to a non-hyperbolic fixed point is also given.",

keywords = "Cobweb diagram, Discrete dynamical systems, Global stability, Isoclines, Root finding algorithm",

author = "Sinan Kap{\c c}ak",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 16th International Conference on Computational Science and Its Applications, ICCSA 2016 ; Conference date: 04-07-2016 Through 07-07-2016",

year = "2016",

doi = "10.1007/978-3-319-42085-1\_4",

language = "English",

isbn = "9783319420844",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer",

pages = "45--53",

editor = "Apduhan, \{Bernady O.\} and Beniamino Murgante and Sanjay Misra and David Taniar and Torre, \{Carmelo M.\} and Rocha, \{Ana Maria A.C.\} and Shangguang Wang and Osvaldo Gervasi and Elena Stankova",

booktitle = "Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings",

address = "Germany",

}

Kapçak, S 2016, Stability of a certain 2-dimensional map with cobweb diagram. in BO Apduhan, B Murgante, S Misra, D Taniar, CM Torre, AMAC Rocha, S Wang, O Gervasi & E Stankova (eds), Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9786, Springer, pp. 45-53, 16th International Conference on Computational Science and Its Applications, ICCSA 2016, Beijing, China, 4/07/16. https://doi.org/10.1007/978-3-319-42085-1_4

Stability of a certain 2-dimensional map with cobweb diagram. / Kapçak, Sinan.
Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings. ed. / Bernady O. Apduhan; Beniamino Murgante; Sanjay Misra; David Taniar; Carmelo M. Torre; Ana Maria A.C. Rocha; Shangguang Wang; Osvaldo Gervasi; Elena Stankova. Springer, 2016. p. 45-53 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9786).

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

TY - GEN

T1 - Stability of a certain 2-dimensional map with cobweb diagram

AU - Kapçak, Sinan

N1 - Publisher Copyright: © Springer International Publishing Switzerland 2016.

PY - 2016

Y1 - 2016

N2 - In this paper, we investigate the following discrete-time map: xn+1 = φ(yn), yn+1 = ψ(xn). We introduce a novel method to determine the stability of the given two-dimensional map by using a one-dimensional map. A cobweb-like diagram is also introduced in order to analyze the stability of the system. We show that the stability of a fixed point in cobweb diagram implies the stability in phase diagram for the given system. In addition, an application of the system to a non-hyperbolic fixed point is also given.

AB - In this paper, we investigate the following discrete-time map: xn+1 = φ(yn), yn+1 = ψ(xn). We introduce a novel method to determine the stability of the given two-dimensional map by using a one-dimensional map. A cobweb-like diagram is also introduced in order to analyze the stability of the system. We show that the stability of a fixed point in cobweb diagram implies the stability in phase diagram for the given system. In addition, an application of the system to a non-hyperbolic fixed point is also given.

KW - Cobweb diagram

KW - Discrete dynamical systems

KW - Global stability

KW - Isoclines

KW - Root finding algorithm

UR - https://www.scopus.com/pages/publications/84978909361

U2 - 10.1007/978-3-319-42085-1_4

DO - 10.1007/978-3-319-42085-1_4

M3 - Conference contribution

AN - SCOPUS:84978909361

SN - 9783319420844

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 45

EP - 53

BT - Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings

A2 - Apduhan, Bernady O.

A2 - Murgante, Beniamino

A2 - Misra, Sanjay

A2 - Taniar, David

A2 - Torre, Carmelo M.

A2 - Rocha, Ana Maria A.C.

A2 - Wang, Shangguang

A2 - Gervasi, Osvaldo

A2 - Stankova, Elena

PB - Springer

T2 - 16th International Conference on Computational Science and Its Applications, ICCSA 2016

Y2 - 4 July 2016 through 7 July 2016

ER -

Kapçak S. Stability of a certain 2-dimensional map with cobweb diagram. In Apduhan BO, Murgante B, Misra S, Taniar D, Torre CM, Rocha AMAC, Wang S, Gervasi O, Stankova E, editors, Computational Science and Its Applications - 16th International Conference, ICCSA 2016, Proceedings. Springer. 2016. p. 45-53. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-319-42085-1_4

Stability of a certain 2-dimensional map with cobweb diagram

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this