Global Dynamics in Chemotaxis-Exclusion Competition Models of Two-Species
The Nuemann initial edge value problem of two group chemotaxis exclusion competition models in two-dimensional smooth bounded regions was studied,and compared with the existing research work,we considered the signal generation function with a more general form.First,we obtained a globally bounded classical solution for any exclusion coefficient problem greater than zero with initial values of certain regularity through classical LP estimation and parabolic equation related regularity theory,that is,‖u‖L∞(Ω),‖v‖L∞(Ω),‖w‖W1,∞(Ω),‖z‖W1,∞(Ω)were less than or equal to a constant.Second,the global asymptotic stability of the constant equilibrium state(u∗,v∗,w∗,z∗)under different parameter conditions in the norm sense of the L∞ was studied by building Lyapunov functionals,that is,‖u‖L∞(Ω),‖v‖L∞(Ω),‖w‖L∞(Ω),‖z‖L∞(Ω)all tended to be a fixed value.Finally,we performed linear stability analysis of the non-zero boundary constant steady state of the model with different signal generation functions,and performed numerical simulation.The results show that different signal generation functions,different repulsion coefficients in chemotaxis-competitive systems can lead to various complex space-time spots around the constant equilibrium state.
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