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Network Biology, 2014, 4(3): 130-150
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Article

A quasi chemical approach for the modeling of predator-prey interactions

Muhammad Shakil1, H. A. Wahab1, Muhammad Naeem2, Saira Bhatti3
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 3 April 2014;Accepted 8 May 2014;Published online 1 September 2014
IAEES

Abstract
We aim to develop the reaction diffusion equation for different types of mechanism of the predator-prey interactions with quasi chemical approach. The chemical reactions representing the interactions obey the mass action law. Since the cell-jump models may be considered as the proper diffusion models by themselves, the territorial animal like fox is given a simple cell as its territory. Under the proper relations between coefficients, like complex balance or detailed balance, this system demonstrated globally stable dynamics.

Keywords quasi-chemical approach;predator-prey interactions;modeling fox and rabbit interactions.



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