WorkshopsTravelling wave solutions of the 3-species Lotka-Volterra competition-diffusion system
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This is a joint work with Chueh-Hsin Chang. The existence of a travelling wave solutions of the 3-species Lotka-Volterra competition-diff usion system is established. A travelling wave solution can be considered as a heteroclinic orbit of a vector fi eld in the six dimensional Euclidean space. Under suitable assumptions on the parameters of the equations, we apply a bifurcation theory 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 pro files 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. As concrete examples of application of our result, we find several explicit regions of the parameters of the equations where the bifurcations of 3-species travelling waves occur.
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Chiun-Chuan Chen
2011-09-01
10:30:00 - 11:20:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
This is a joint work with Chueh-Hsin Chang. The existence of a travelling wave solutions of the 3-species Lotka-Volterra competition-diff usion system is established. A travelling wave solution can be considered as a heteroclinic orbit of a vector fi eld in the six dimensional Euclidean space. Under suitable assumptions on the parameters of the equations, we apply a bifurcation theory 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 pro files 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. As concrete examples of application of our result, we find several explicit regions of the parameters of the equations where the bifurcations of 3-species travelling waves occur.
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