On Target-Oriented Control of Henon and Lozi maps
Elena Braverman, Alexandra Rodkina
TL;DR
This paper investigates stabilizing nonlinear difference equations, specifically Hénon and Lozi maps, using modified Target-Oriented Control in both deterministic and stochastic contexts, analyzing the impact of randomness in control parameters.
Contribution
It introduces a modified Target-Oriented Control method for stabilizing Hénon and Lozi maps, including stochastic effects, which is a novel approach for these systems.
Findings
Successful stabilization of Hénon and Lozi maps using the proposed control.
Analysis of stochastic components' influence on control effectiveness.
Validation of control method through numerical experiments.
Abstract
We explore stabilization for nonlinear systems of difference equations with modified Target-Oriented Control and a chosen equilibrium as a target, both in deterministic and stochastic settings. The influence of stochastic components in the control parameters is explored. The results are tested on the H\'{e}non and the Lozi maps.
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