This paper emphasizes the effect of spillovers on R&D (Research and Development) level. When competing firms have spillovers to each other in R&D, cooperation will always increase fi...This paper emphasizes the effect of spillovers on R&D (Research and Development) level. When competing firms have spillovers to each other in R&D, cooperation will always increase firms' profits. Only if the positive spillover is large enough, the cooperative R&D level will be larger than the non\|cooperative R&D level. The cooperative level will be smaller than the non\|cooperative level if the positive spillover is small enough. However, the cooperative level is always smaller than the non\|cooperative level while there're negative spillovers to each other. R&D levels are the function of the spillover and will change with the spillover. The changing regularity is related to the sign of spillover and to whether they're cooperative or not. Spillovers made by the competing firms are usually different. When spillovers are small enough, the larger the spillover obtained from the other, the smaller the firm will invest in R&D; inversely, when the spillover is large enough, the larger spillovers obtains from the other, the larger the firm will invest in R&D.展开更多
By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x ...By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.展开更多
文摘This paper emphasizes the effect of spillovers on R&D (Research and Development) level. When competing firms have spillovers to each other in R&D, cooperation will always increase firms' profits. Only if the positive spillover is large enough, the cooperative R&D level will be larger than the non\|cooperative R&D level. The cooperative level will be smaller than the non\|cooperative level if the positive spillover is small enough. However, the cooperative level is always smaller than the non\|cooperative level while there're negative spillovers to each other. R&D levels are the function of the spillover and will change with the spillover. The changing regularity is related to the sign of spillover and to whether they're cooperative or not. Spillovers made by the competing firms are usually different. When spillovers are small enough, the larger the spillover obtained from the other, the smaller the firm will invest in R&D; inversely, when the spillover is large enough, the larger spillovers obtains from the other, the larger the firm will invest in R&D.
文摘By using a new method, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions for three\|species Lotka\|Volterra mixed systems with periodic stocking:x 1′(t)=x 1(t)(b 1(t)-a 11 (t)x 1(t)-a 12 (t)x 2(t)-a 13 (t)x 3(t))+S 1(t) x 2′(t)=x 2(t)(-b 2(t)+a 21 (t)x 1(t)-a 22 (t)x 2(t)-a 23 (t)x 3(t))+S 2(t) x 3′(t)=x 3(t)(-b 3(t)+a 31 (t)x 1(t)-a 32 (t)x 2(t)-a 33 (t)x 3(t))+S 3(t)where b i(t),a ij (t)(i,j=1,2,3) are positive continuous T \|periodic functions, S i(t)(i=1,2,3) are nonnegative continuous T \|periodic functions.
