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Network Biology, 2015, 5(4): 169-179
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Article

The predator-prey models for the mechanism of autocatalysis, pair wise interactions and movements to free places

Muhammad Shakil1, H. A. Wahab1, Muhammad Naeem2, Saira Bhatti3, Muhammad Shahzad1
1Department of Mathematics, Hazara University, Manshera, Pakistan
2Department of Information Technology, Hazara University, Manshera, Pakistan
3Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

Received 19 November 2015;Accepted 25 December 2015;Published online 1 December 2015
IAEES

Abstract
In this paper we aim to develop the modeled equations for different types of mechanism of the predator-prey interactions with the help of a quasi chemical approach while taking a special study case of foxes and rabbits, these mechanisms include autocatalysis mechanism, pair wise interactions and the mechanism of their movements to some free places. The chemical reactions representing the interactions obey the mass action law. The territorial animal like fox is assigned a simple cell as its territory. Under the proper relations between coefficients, this system may demonstrate globally stable dynamics.

Keywords predator prey interactions;autocatalysis mechanism;modeling of fox and rabbit interaction.



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