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A problem of local and global attractors in bounded reaction systems

Consider the discretized system of 5 dimensional SIRS model
$\dot x_1 = -kx_1 + kxy_5$
$\dot x_2 = -ax_2 – cx_1$
$\dot x_3 = kx_1 + kxy_5$
$\dot x_4 = -cx_2$
$\dot x_5 = -kx_1 – kxy_5$
where $k, a, c, k_2, k_5$ are positive constants and $x_1,x_2,\dots,x_5$ are the corresponding state variables.
I found the set of equilibrium points of this system
$$(0,0,0,0,0)$$$$(1,0,0,0,0)$$$$(0,0,0,1,0)$$$$(1,0,0,0,1)$$$$(0,0,1,0,0)$$$$(0,1,0,0,0)$$$$(1,0,1,0,0)$$$$(0,0,0,0,0)$$$$(0,1,0,0,0)$$$$(0,0,0,0,0)$$$$(0,1,1,0,0)$$$$(0,0,0,0,0)$$$$(0,0,0,0,0)$$$$(1,0,0,0,0)$$$$(0,1,0,0,0)$$$$(0,0,1,0,0)$$$$(0,0,1,0,0)$$$$(0,0,0,0,0)$$$$(0,1,0,0,0)$$$$(0,1,0,0,0)$$$$(0,0,0,0,0)$$$$(0,0,0
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