we consider the Lotka-Volterra competition system with dynamical resources and density-dependent diffusion。We show that the system has a unique global classical solution when initial datum is in some appropriate functional space.  By constructing appropriate Lyapunov functionals and using LaSalle's invariant principle, we prove that the solution converges to the co-existence steady state exponentially or competitive exclusion steady state algebraically as time tends to infinity in different parameter regimes. Our results reveal that once the resource species has temporal dynamics, the striking phenomenon “slower diffuser always prevails”for given spatially heterogeneous resource no longer exist and two competitors can coexist regardless of their diffusion rates and initial values. When the prey resource is spatially heterogeneous, we use numerical simulations to demonstrate that the phenomenon “slower diffuser always prevails”breaks down if the non-random dispersion strategy amongst competing species is employed.

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