Figure 1

The blue curves are the prey-nullclines and the red lines are the predator-isoclines. The four figures are the possible plots of predator-nullcline for four different values of c . (a) For \(c = 0.2\), two nullclines do not intersect at any point in the interior of the feasible domain (the prey nullcline is below the predator nullcline), suggesting there is no equilibrium point; (b) as we increase the slope of predator-nullcline, the two equilibria approach each other and collide for \(c = 0.28\) and consequently, there is one equilibrium point; (c) for \(c=0.3\), both the nullclines cross twice, suggesting there are two equilibrium points; (d) for \(c=2\), the prey nullcline is unbounded and has two vertical asymptotes \(x = x_{\pm}\) shown by black lines. The other parameter values are \(r=0.8\), \(K=5\), \(q=0.2\), \(a=2\), \(b=0.4\), \(d=0.1\), \(e=0.2\), \(m=2\).