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| 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: |
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| title | Existence of periodic solutions in predator prey and competition dynamic systems |
| contributor.author | Bohner, Martin |
| contributor.author | Fan, Meng |
| contributor.author | Zhang, Jimin |
| contributor.deptlab | Mathematics & Statistics |
| subject | Beddington–DeAngelis response |
| subject | Coincidence degree |
| subject | Competition system |
| subject | Gilpin–Ayala system |
| subject | Holling-type response |
| subject | Periodic solution |
| subject | Predator–prey system |
| subject | Time scales |
| date.issued | 2006 |
| publisher | Elsevier |
| identifier.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). |
| identifier.pub.URI | |
| description.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 |
| type.DCMIType | text |
| type.status | Final version |
| rights | 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. |
| rights.URI | |
| relation.isPartOf | Non Linear Analysis: Real World Applications |
| date.accessioned | 2007-04-11T17:00:48Z |
| date.available | 2008-04-22T17:36:43Z |
| identifier.persist.URI |