# Null controllability of a cascade model in population dynamics

## TL;DR

This paper proves that it is possible to steer prey-predator population models to extinction within finite time using a single control force, by developing new inequalities for the system.

## Contribution

It introduces a novel Carleman inequality for the adjoint system of a cascade population model with boundary degeneracy, enabling null controllability results.

## Key findings

- Existence of a control force that drives populations to extinction
- Development of a Carleman inequality for degenerate systems
- Establishment of an observability inequality for the model

## Abstract

In this paper, we are concerned with the null controllability of a linear population dynamics cascade systems (or the so-called prey-predator models) with two different dispersion coefficients which degenerate in the boundary and with one control force. We develop first a Carleman type inequality for its adjoint system, and then an observability inequality which allows us to deduce the existence of a control acting on a subset of the space domain which steers both populations of a certain age to extinction in a finite time.