本計劃證明類捕食-食餌反應擴散系統之行波解的存在性。該系統的非線性項為數個單調函數的乘積，其波方程為四維的常微風方程。利用高維度的象空間分析、Wazewski 定理與Lyaounov函數，證明行波解的存在性。此研究成果可以直接應用在一些生態模型。 In this project we investigate the existence of traveling wave solutions for a class of diffusive predator–prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalle?Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.
