Figure 1

The blue line represents prey nullcline and the black line represents predator nullcline, (a) when \(k=1\), \(m=0.03\), there is no interior equilibrium point. (b) Fixing \(k=1\) and varying m shows that system (2.4a)–(2.4b) has a unique equilibrium \(E_{1}\) in blue dot, two interior equilibria \(E_{2}\), \(E_{3}\) in black dot, one equilibrium \(E_{3}\) coincides with \(E_{0}\) and has a unique interior equilibrium \(E_{4}\) in red dot for \(m=c\), \(E_{3}\) disappears and \(E_{5}\) is given in red dot for \(m>c\). (c) Taking \(m=0.08586\), the scenario for the existence of no equilibria, unique equilibrium, and two equilibria by varying fear parameter k