Rich Dynamics of a Predator-Prey System with Different Kinds of Functional Responses

Figure 2

The stability region of the trivial singular state , boundary singular state , and the coexisting singular state of (4), in the parameter-space where and . Other parameter values are , , , , and . In the figure, (i) within the blue colored region, the equilibrium point is locally asymptotically stable, but boundary singular point and the interior equilibrium are unstable; (ii) within the green colored region, the equilibrium point is locally asymptotically stable, but trivial equilibria and interior equilibrium are unstable; and (iii) within the red colored region, the interior equilibrium point is locally asymptotically stable, but the trivial equilibrium and boundary equilibrium are unstable.