Local Stability Theory for Caputo Fractional Planar System and
Application to Predator-Prey Model with Group Defense
Abstract
In this manuscript we show a new approach into analyzing the local
stability of equilibrium points of non-linear Caputo fractional planar
systems. It is shown that the equilibrium points of such systems can
exhibit an unstable focus or stable focus under suitable conditions.
Further, it is shown that for $\alpha$ close to $1,$
global stability can be concluded, under suitable conditions, and
without the use of a Lyapunov function. Lastly, our results are applied
to a predator prey model with group defense, in which we show that it
had equilibrium points that undergo an unstable focus and a stable
focus.