A large class of stochastic differential games for several players is considered in this paper.The class includes Nash differential games as well as Stackelberg differential games.A mix is possible.The existence of fe...A large class of stochastic differential games for several players is considered in this paper.The class includes Nash differential games as well as Stackelberg differential games.A mix is possible.The existence of feedback strategies under general conditions is proved.The limitations concern the functionals in which the state and the controls appear separately.This is also true for the state equations.The controls appear in a quadratic form for the payoff and linearly in the state equation.The most serious restriction is the dimension of the state equation,which cannot exceed 2.The reason comes from PDE(partial differential equations) techniques used in studying the system of Bellman equations obtained by Dynamic Programming arguments.In the authors' previous work in 2002,there is not such a restriction,but there are serious restrictions on the structure of the Hamiltonians,which are violated in the applications dealt with in this article.展开更多
We consider a system of partial differential equations that describes the interaction of the sterile and fertile species undergoing the sterile insect release method （SIRM）. Unlike in the previous work [M. A. Lewis ...We consider a system of partial differential equations that describes the interaction of the sterile and fertile species undergoing the sterile insect release method （SIRM）. Unlike in the previous work [M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release, Math. Biosci. 5 （1992） 221 247] where the habitat is assumed to be the one-dimensional whole space ~, we consider this system in a bounded one- dimensional domain （interval）. Our goal is to derive sufficient conditions for success of the SIRM. We show the existence of the fertile-free steady state and prove its stability. Using the releasing rate as the parameter, and by a saddle-node bifurcation analysis, we obtain conditions for existence of two co-persistence steady states, one stable and the other unstable. Biological implications of our mathematical results are that： （i） when the fertile population is at low level, the SIRM, even with small releasing rate, can successfully eradicate the fertile insects; （ii） when the fertile population is at a higher level, the SIRM can succeed as long as the strength of the sterile releasing is large enough, while the method may also fail if the releasing is not sufficient.展开更多
基金supported by DAAD-PPP Hong Kong/Germany (No. G. HK 036/09)
文摘A large class of stochastic differential games for several players is considered in this paper.The class includes Nash differential games as well as Stackelberg differential games.A mix is possible.The existence of feedback strategies under general conditions is proved.The limitations concern the functionals in which the state and the controls appear separately.This is also true for the state equations.The controls appear in a quadratic form for the payoff and linearly in the state equation.The most serious restriction is the dimension of the state equation,which cannot exceed 2.The reason comes from PDE(partial differential equations) techniques used in studying the system of Bellman equations obtained by Dynamic Programming arguments.In the authors' previous work in 2002,there is not such a restriction,but there are serious restrictions on the structure of the Hamiltonians,which are violated in the applications dealt with in this article.
基金Part of this work was completed when the second author was visiting the Univer- sity of Western Ontario, and he would like to thank the staff in the Department of Applied Mathematics for their help and thank the University for its excellent facilities and support during his stay. The second author was supported by China Scholarship Council, partially sup- ported by NNSF of China （No. 11031002）, by the Heilongjiang Provincial Natural Science Foundation （No. A200806）, and by the Program of Excellent Team and the Science Research Foundation in Harbin Institute of Technology.
文摘We consider a system of partial differential equations that describes the interaction of the sterile and fertile species undergoing the sterile insect release method （SIRM）. Unlike in the previous work [M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release, Math. Biosci. 5 （1992） 221 247] where the habitat is assumed to be the one-dimensional whole space ~, we consider this system in a bounded one- dimensional domain （interval）. Our goal is to derive sufficient conditions for success of the SIRM. We show the existence of the fertile-free steady state and prove its stability. Using the releasing rate as the parameter, and by a saddle-node bifurcation analysis, we obtain conditions for existence of two co-persistence steady states, one stable and the other unstable. Biological implications of our mathematical results are that： （i） when the fertile population is at low level, the SIRM, even with small releasing rate, can successfully eradicate the fertile insects; （ii） when the fertile population is at a higher level, the SIRM can succeed as long as the strength of the sterile releasing is large enough, while the method may also fail if the releasing is not sufficient.
