Abstract

As one of the most important achievements in nonlinear science, population system has drawn wide attention and extensive research in the past few decades. However, population control is a systematic social project with much complexity for the reason that it involves knowledge in many aspects, such as functional analysis, differential equations, partial differential equations, operator theory. Through initiating a series of groundbreaking work on the issue of population control in China, our scientific workers have made a lot of achievements, which are valuable in terms of theory and practice, in understanding and addressing this issue in a correct way.

To conduct intensive research on the issue of optimal control is a right way to achieve that. They have made strict and detailed analysis to population system, whose results have a great influence on the family planning policy in China.

This paper starts from deducing the population equation and explaining its parameters meaning. Next, it gives the answer to a simple model. Based on stationary population model, this paper, considering population mortality and gaining factor (can only depend on age), gives its prediction to a more general case and tries to gain the optimal control towards population.

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