We propose an efficient numerical method for two population models, based on the nonstandard finite difference （NSFD） schemes and composition methods with complex time steps. The NSFD scheme is able to give positive...We propose an efficient numerical method for two population models, based on the nonstandard finite difference （NSFD） schemes and composition methods with complex time steps. The NSFD scheme is able to give positive numerical solutions that satisfy the conservation law, which is a key property for biological population models. The accuracy is improved by using the composition methods with complex time steps. Numerical tests on the plankton nutrient model and whooping cough model are presented to show the efficiency and advantage of the proposed numerical method.展开更多
A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochasti...A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.展开更多
文摘We propose an efficient numerical method for two population models, based on the nonstandard finite difference （NSFD） schemes and composition methods with complex time steps. The NSFD scheme is able to give positive numerical solutions that satisfy the conservation law, which is a key property for biological population models. The accuracy is improved by using the composition methods with complex time steps. Numerical tests on the plankton nutrient model and whooping cough model are presented to show the efficiency and advantage of the proposed numerical method.
基金This work was supported by the National Natural Science Foundation of P. R. China （No. 11171081, 11171056）, the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology （No. HIT.NSRIF.2011094）, and the Scientific Research Foundation of Harbin Institute of Technology at Weihai （No. HIT （WH） ZB201103）.
文摘A stochastic two-species Schoener＇s competitive model is proposed and investigated. Sufficient conditions for the existence of global positive solutions, boundedness~ uniform continuity, global attractivity stochastic permanence and extinction are obtained. More- over, the upper-growth rate and the average in time of the sample paths of solutions are also estimated. Finally, some figures are introduced to illustrate the main results.
