In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At t...In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At the same time, the dynamic behaviors between systems with diffusion and those without diffusion are compared. This shows the influence of diffusions on the persistence of species.展开更多
The persistence exponent <img src="Edit_8589f062-08af-48bf-9fa4-ea64e4f98789.png" alt="" /> for the simple diffusion equation <img src="Edit_8bd8b3b8-7f1f-4ea5-a5f5-c5ccc20288f4.png&q...The persistence exponent <img src="Edit_8589f062-08af-48bf-9fa4-ea64e4f98789.png" alt="" /> for the simple diffusion equation <img src="Edit_8bd8b3b8-7f1f-4ea5-a5f5-c5ccc20288f4.png" alt="" /> , with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field <img src="Edit_cc47d602-457a-4e52-93d8-acc18dcaf933.png" alt="" /> at a specified spatial coordinate remains positive throughout for a certain time<em> t</em> behaves as <img src="Edit_aacdd656-f2c2-4cde-ba3c-1b32bf053b3b.png" alt="" /> for asymptotically large time <em>t</em>. The value of <img src="Edit_77272c69-2a19-4918-a183-7db96b262c7a.png" alt="" /> , calculated here for any integer dimension <em>d</em>, is <img src="Edit_bc64e52a-d6d0-4b63-8ef3-aa0f9d3c39cc.png" alt="" /> for <img src="Edit_becf7ae7-0ae4-43a6-9a41-017f25747517.png" alt="" /> and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values <img src="Edit_fbefbfcf-d76b-4eeb-a5f5-d8afda4a1a0c.png" alt="" /> for <img src="Edit_ec927d57-c273-40dd-8126-706443b57534.png" alt="" /> respectively.展开更多
文摘In this paper, the stabilities of boundary equilibrium and positive equilibrium of two_species Ayala competitive systems with two different diffusions are discussed, and dynamic behaviors of species are obtained. At the same time, the dynamic behaviors between systems with diffusion and those without diffusion are compared. This shows the influence of diffusions on the persistence of species.
文摘The persistence exponent <img src="Edit_8589f062-08af-48bf-9fa4-ea64e4f98789.png" alt="" /> for the simple diffusion equation <img src="Edit_8bd8b3b8-7f1f-4ea5-a5f5-c5ccc20288f4.png" alt="" /> , with random Gaussian initial condition, has been calculated exactly using a method known as selective averaging. The probability that the value of the field <img src="Edit_cc47d602-457a-4e52-93d8-acc18dcaf933.png" alt="" /> at a specified spatial coordinate remains positive throughout for a certain time<em> t</em> behaves as <img src="Edit_aacdd656-f2c2-4cde-ba3c-1b32bf053b3b.png" alt="" /> for asymptotically large time <em>t</em>. The value of <img src="Edit_77272c69-2a19-4918-a183-7db96b262c7a.png" alt="" /> , calculated here for any integer dimension <em>d</em>, is <img src="Edit_bc64e52a-d6d0-4b63-8ef3-aa0f9d3c39cc.png" alt="" /> for <img src="Edit_becf7ae7-0ae4-43a6-9a41-017f25747517.png" alt="" /> and 1 otherwise. This exact theoretical result is being reported possibly for the first time and is not in agreement with the accepted values <img src="Edit_fbefbfcf-d76b-4eeb-a5f5-d8afda4a1a0c.png" alt="" /> for <img src="Edit_ec927d57-c273-40dd-8126-706443b57534.png" alt="" /> respectively.
