On the Extinction-Free Stabilization of Predator-Prey Dynamics

Scientists have long been attracted to mechanisms surrounding the predator-prey system. The Lotka-Volterra (LV) model is the most popular formalism used to investigate the dynamics of this system. LV equations present non-linear dynamics that exhibit periodic oscillations in both prey and predator populations. In practical situations, it is useful to stabilise the system asymptotically to a desired set point (population) wherein the two species coexist by fashioning specific control actions. This control strategy can be beneficial for problems that can arise when there is a risk of extinction of one of the species and human intervention must be planned. One natural and well-established theory for describing systems obeying energy balance laws is the port-Hamiltonian modeling, an extension of classical Hamiltonian mechanics to systems endowed with control and observation. The LV model can be formally represented as a non-linear mechanical oscillator employing the canonical equations of Hamilton. This special mathematical structure aids planning and designing efficient control actions. The proposed strategy employs a systematic procedure to efficiently plan biological control actions and bypass species extinction through asymptotic stabilisation of populations.