Dynamics Twin Cannibalism of Two Predator and Two Prey System with Prey Defense

Abstract

The study discusses the condition of the existence of all non-negative equilibrium points. There are 9 realistic equilibrium points from the constructed model. A local stable condition is obtained, a point of equilibrium that is completely biologically feasible. The analytical method on the mathematically formed model is limited, so numerical simulation is also given to explore the model. Numerical simulation is intervened in a model that will show growth in trajectories. The tendency of trajectories in prey one and predator one species is relatively the same because the interactions that occur are intensive. Likewise, prey two and predator two occur, and the interactions that occur cause population growth grow to fluctuate. Differences occur in both types of species, namely predator-prey one and predator-prey two. In the one interaction group, growth tends to be more volatile and moves slowly towards the point of stability in population growth. Incidence is inversely proportional to the interaction of species two which tend to be faster towards the stability point. In general, the results of numerical simulations show that there is a pattern formation in the predator-prey system that grows sustainabley.