Missouri S&T Scholar's Mine Research RepositoryMissouri S&T Research
print 
Title: Existence of periodic solutions in predator prey and competition dynamic systems
Author (s): Bohner, Martin
Fan, Meng
Zhang, Jimin
Department/Lab Affiliations: Mathematics & Statistics
Keywords: Beddington–DeAngelis response
Coincidence degree
Competition system
Gilpin–Ayala system
Holling-type response
Periodic solution
Predator–prey system
Time scales
Issue Date: 2006
Publisher: Elsevier
Citation: Bohner, Martin., Fan, Meng., and Zhang, Jimin. "Existence of Periodic Solutions in Predator Prey and Competition Dynamic Systems." Non Linear Analysis: Real World Applications, vol. 7, no. 5, (2006).
Abstract: In this paper, we systematically explore the periodicity of some dynamic equations on time scales, which incorporate as special cases many population models (e.g., predator–prey systems and competition systems) in mathematical biology governed by differential equations and difference equations. Easily verifiable sufficient criteria are established for the existence of periodic solutions of such dynamic equations, which generalize many known results for continuous and discrete population models when the time scale View the MathML source is chosen as View the MathML source or View the MathML source, respectively. The main approach is based on a continuation theorem in coincidence degree theory, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in dynamic equations on time scales. This study shows that it is unnecessary to explore the existence of periodic solutions of continuous and discrete population models in separate ways. One can unify such studies in the sense of dynamic equations on general time scales.
Type: Article - Journal
text
In Title: Non Linear Analysis: Real World Applications
Copyright Notice: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
FULL COPYRIGHT INFORMATION:
http://www.elsevier.com/wps/find/authorsview.authors/authorsrights
Publisher URL:
http://dx.doi.org/10.1016/j.nonrwa.2005.11.002
Link to this page:
http://scholarsmine.mst.edu/post_prints/Existenceofperiodicsolutionsinpredatorpreyandco_09007dcc804e7f2d.html



titleExistence of periodic solutions in predator prey and competition dynamic systems
contributor.authorBohner, Martin
contributor.authorFan, Meng
contributor.authorZhang, Jimin
contributor.deptlabMathematics & Statistics
subjectBeddington–DeAngelis response
subjectCoincidence degree
subjectCompetition system
subjectGilpin–Ayala system
subjectHolling-type response
subjectPeriodic solution
subjectPredator–prey system
subjectTime scales
date.issued2006
publisherElsevier
identifier.citationBohner, Martin., Fan, Meng., and Zhang, Jimin. "Existence of Periodic Solutions in Predator Prey and Competition Dynamic Systems." Non Linear Analysis: Real World Applications, vol. 7, no. 5, (2006).
identifier.pub.URI
http://dx.doi.org/10.1016/j.nonrwa.2005.11.002
description.abstractIn this paper, we systematically explore the periodicity of some dynamic equations on time scales, which incorporate as special cases many population models (e.g., predator–prey systems and competition systems) in mathematical biology governed by differential equations and difference equations. Easily verifiable sufficient criteria are established for the existence of periodic solutions of such dynamic equations, which generalize many known results for continuous and discrete population models when the time scale View the MathML source is chosen as View the MathML source or View the MathML source, respectively. The main approach is based on a continuation theorem in coincidence degree theory, which has been extensively applied in studying existence problems in differential equations and difference equations but rarely applied in dynamic equations on time scales. This study shows that it is unnecessary to explore the existence of periodic solutions of continuous and discrete population models in separate ways. One can unify such studies in the sense of dynamic equations on general time scales.
typeArticle - Journal
type.DCMITypetext
type.statusFinal version
rightsThis material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
rights.URI
http://www.elsevier.com/wps/find/authorsview.authors/authorsrights
relation.isPartOfNon Linear Analysis: Real World Applications
date.accessioned2007-04-11T17:00:48Z
date.available2008-04-22T17:36:43Z
identifier.persist.URI
http://scholarsmine.mst.edu/post_prints/Existenceofperiodicsolutionsinpredatorpreyandco_09007dcc804e7f2d.html