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Abstract: The predator-prey relationship is not only a fundamental relation between species in nature, but also very important in ecology and bio-mathematics. In most research fields, which deal with definite objects, the traditional approach is to derive some basic rules based on experiments and observations, then to obtain mathematical equations and their analytical solutions. Numerical solutions are commonly required due to the difficulties to obtain analytical solutions. But analytical solutions have important merits in theory, especially as the benchmark solutions to check the accuracy, the convergence and the stability of various numerical computational methods and to improve their difference schemes, grid generations and so on. Some exact analytical solutions of a ratio-dependent capture predator-prey system with Holling type III functional response are derived in this paper. They can be used as the benchmark solutions to verify the numerical solutions and even to develop various numerical methods.
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Received: 15 October 2009
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2010, Vol. 28 
