تحليل الاستقرار لنظام فولتيرا – لوتكا بنمو لوجيستي باستخدام طريقتي ليابونوف
Abstract
النماذج الرياضية للتنافس بين الأنواع هي من بين المسائل الهامة لديناميكا السكان بعدة أنواع. في هذه المقالة، نجري تحليلا رياضيا موضحا بأشكال بيانية باستخدام Matlab لإعطاء تبصر عن حالة التعايش بين نوعين يخضعان لنظام فولتيرا – لوتكا بنمو لوجيستي, كما نقدم تحليل الاستقرار لنظام فولتيرا – لوتكا بنمو لوجيستي باستخدام طريقتي ليابونوف الأولى والثانية. نقترح في طريقة ليابونوف الثانية تابع ليابونوف جديداً يخص النموذج المدروس. نجري العديد من تجارب المحاكاة الحاسوبية باستخدام نظام جبر الحاسوب Matlab لتوضيح سلوك النظام المدروس على المدى الطويل.
The mathematical models of competition between species are one of the most important problems for population dynamics with multi species. In this paper, we give stability analysis for a Lotka-Volterra system with logistic growth by Lyapunov methods. We also present new Lyapunov functions for second Lyapunov method. Many numerical simulations have been carried out on computer algebra system: Maple and Matlab to illustrate the behavior of the considered system for a long time.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
The authors retain the copyright and grant the right to publish in the magazine for the first time with the transfer of the commercial right to the Tishreen University Journal -Basic Sciences Series
Under a CC BY- NC-SA 04 license that allows others to share the work with of the work's authorship and initial publication in this journal. Authors can use a copy of their articles in their scientific activity, and on their scientific websites, provided that the place of publication is indicted in Tishreen University Journal -Basic Sciences Series . The Readers have the right to send, print and subscribe to the initial version of the article, and the title of Tishreen University Journal -Basic Sciences Series Publisher
journal uses a CC BY-NC-SA license which mean
You are free to:
- Share — copy and redistribute the material in any medium or format
- Adapt — remix, transform, and build upon the material
- The licensor cannot revoke these freedoms as long as you follow the license terms.
- Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- NonCommercial — You may not use the material for commercial purposes.
- ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.