I want to plot the phase diagram of prey predator versus prey refuge to see how the prey refuge influences the population of prey and predator. And this is the system
$x'=\alpha x(1-x/k)-\beta\frac{(1-m)xy}{1+a(1-m)x}-q_1E_1x$
$y'=-\gamma y+c\beta\frac{(1-m)xy}{1+a(1-m)x}-q_2E_2y$
The prey predator with Holling type II model is incorporating a prey refuge, $mx$ and $k$, $\alpha$, $\gamma$, $c$ and $\beta/\alpha$ are the carrying capacity, growth rate of prey, death rate of predator, conversion factor denoting the number of newly born predators for each captured prey and maximum number of prey that can be eaten by each predator in unit time respectively.
I have the numerical value for $a=0.02$, $k=100$, $\alpha=10$, $\beta=0.6$, $\gamma=0.09$, $c=0.02$.
Thanks so much!
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