Figure 5: The results for the coupling proportional to the energy density of DE by fixing the local abundance. Figure 6: The results for the coupling proportional to the energy density of DM by fixing the local abundance. 0 1 2 3 4 5 10 15 20 25 30 35 40 W=−0.96, $_{1}$=0,Ce$^{2}$=1 Normalized  8 CDM $_{2}$=0.01 $_{2}$=0.01 $_{2}$=−0.03 $_{2}$=−0.03 $_{2}$=−0.05 $_{2}$=−0.05 10$^{13}$<M/(h$^{−1}$M$_{s}$)<10 14 z dN/dz/10 6 0 0.5 1 1.5 2 5 10 15 20 25 30 W=−0.96, $_{1}$=0,Ce$^{2}$=1 Normalized  8 CDM $_{2}$=0.01 $_{2}$=0.01 $_{2}$=−0.03 $_{2}$=−0.03 $_{2}$=−0.05 $_{2}$=−0.05 10$^{15}$<M/(h$^{−1}$M$_{s}$)<10 16 z dN/dz/10 (a) (b) 0 1 2 3 4 5 10 15 20 25 30 35 40 W=−1.04, $_{2}$=0,Ce$^{2}$=1 Normalized  8 CDM $_{1}$=0.0001 $_{1}$=0.0001 $_{1}$=0.0003 $_{1}$=0.0003 $_{1}$=0.0005 $_{1}$=0.0005 10$^{13}$<M/(h$^{−1}$M$_{s}$)<10 14 z dN/dz/10 6 0 1 2 3 4 50 100 150 W=−1.04, $_{2}$=0,Ce$^{2}$=1 Normalized  8 CDM $_{1}$=0.0001 $_{1}$=0.0001 $_{1}$=0.0003 $_{1}$=0.0003 $_{1}$=0.0005 $_{1}$=0.0005 10$^{14}$<M/(h$^{−1}$M$_{s}$)<10 15 z dN/dz/10 4 (a) (b) VI. CONCLUSIONS AND DISCUSSIONS Assuming first that DE component is homogeneous, we have investigated how DM approaches the dynamical equilibrium in the collapsing system. In the presence of coupling between DE and DM, the flow of mass and energy between the components changes the time required by the system to reach equilibrium and also the equilibrium configuration itself. Our discussion is based on the perturbation theory developed in [8, 19]. We reproduce the 19