پایداری و بقا در یک مدل ریاضی از تاثیر متقابل منابع آبی و جمعیت بر یکدیگر

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشیار دانشکده ریاضی و آمار دانشگاه بیرجند

2 دانشگاه بیرجند، بیرجند، ایران

چکیده

در این مقاله با معرفی یک مدل ریاضی مبتنی بر دستگاه‎­ ‎های شکار و شکارچی، به مطالعه‎­ی تاثیر متقابل جمعیت و منابع آبی بر یکدیگر خواهیم پرداخت. ابتدا یک مدل ریاضی در قالب یک معادله‎ی دیفرانسیل را معرفی می­کنیم و سپس توابع و پارامترهای موثر در این فرایند را معرفی خواهیم کرد. همچنین به مطالعه‎ی رفتار موضعی دستگاه پیرامون نقاط تعادل درونی و همچنین مطالعه‎­‎ی رفتار سراسری دستگاه در ناحیه‎­‎ی قابل قبول برای جواب­‎ها خواهیم پرداخت. به ویژه نشان خواهیم داد که چگونه تغییرات پارامترهای موثر بر دستگاه می‎­‎توانند با ایجاد انشعاب‎های موضعی و تغییر در ساختار مدار­‎ها، منجر به بقا یا عدم بقای جمعیت نسبت به یک وضعیت تعادل شوند.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Stability and Permanency in a mathematical model for reciprocal effect of water resources and population

نویسندگان [English]

  • omid rabieimotlagh 1
  • Hajimohammad Mohammadinejad 2
1 associate professor/Faculty of Mathematics and Statistics University of Birjand
2 University of Birjand, Birjand, Iran
چکیده [English]

In this paper, we will introduce a mathematical model, based on prey-predator models, to study reciprocal effects of water resources and population. First, we will construct the model and introduce the parameters and variables of the system. Next we will study local behaviors around inner equilibrium points and global behaviors in the admissible region of the system. Especially we will see that how changes of the parameters might cause simultaneous permanency/impermanency of population and water resources through local bifurcations and changes in the structure of solutions

کلیدواژه‌ها [English]

  • Permanency
  • Prey-Predator systems
  • local bifurcations
  • water resources
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