In this paper, a prey-predator system incorporating prey
refuge and predator cannibalism is studied. The stability and ultimate
boundedness of the analyzed state parameters (𝑦1, 𝑦2) defining the system are obtained using the
Lyapunov’s second or direct method. We construct a suitable complete Lyapunov
function for the nonlinear system and demonstrate its efficacy. The method is
built upon applying various theoretical Lyapunov functions. By constructing a
Lyapunov function which possesses a functional relationship to the the original
model system, we give sufficient conditions which ensure the stability and
ultimate boundedness of the state parameters describing the nonlinear prey-predator
system. We give a numeric example to illustrate the result obtained.
JEL classification numbers: 34C27, 34D23, 34C25.
Keywords: Prey-predator system, Prey refuge, Predator cannibalism, Stability, Boundedness,