| Abstract: |
| In population ecology, coexistence and exclusion are central problems for competiting species. Travelling wave solution can be partially used to answer the question about the competition behavior between species. In this talk, we consider the travelling waves of the 3-species Lotka-Volterra competition-diffusion systems. Such a travelling wave solution can be considered as a heteroclinic orbit of a vector field in R^6. Under suitable assumptions on the parameters of the equations, we apply bifurcation theories of heteroclinic orbits to show that a 3-species travelling wave can bifurcate from two 2-species waves which connect to a common equilibrium. The three components of the 3-species wave obtained are positive and have the profiles that one component connects a positive state to zero, one component connects zero to a positive state, and the third component is a pulse between the previous two with a long middle part close to a positive constant. This is a joint work with Professor Chiun-Chuan Chen. |
|