# Stabilization of structured populations via vector target oriented control

## TL;DR

This paper introduces a new control method for stabilizing structured population models, effectively managing chaos and stabilizing periodic solutions in complex discrete systems like the LPA and delayed Ricker models.

## Contribution

The paper develops a novel target oriented control approach for structured population models, enabling stabilization of states and periodic solutions in higher-order and delayed systems.

## Key findings

- Successfully stabilizes chaotic dynamics in structured populations.
- Extends control techniques to higher-order and delayed difference equations.
- Demonstrates effectiveness on LPA and delayed Ricker models.

## Abstract

In contrast with unstructured models, structured discrete population models have been able to fit and predict chaotic experimental data. However, most of the chaos control techniques in the literature have been designed and analyzed in a one-dimensional setting. Here, by introducing target oriented control for discrete dynamical systems, we prove the possibility to stabilize a chosen state for a wide range of structured population models. The results are illustrated with introducing a control in the celebrated LPA model describing a flour beetle dynamics. Moreover, we show that the new control allows to stabilize periodic solutions for higher order difference equations, such as the delayed Ricker model, for which previous target oriented methods were not designed.