On target-oriented control of Hénon and Lozi maps

Braverman, Elena; Rodkina, Alexandra

doi:10.1080/10236198.2022.2088286

Cited by 4 publications

(1 citation statement)

References 39 publications

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“…To really reveal the strange structure of the Hénon attractor, Lozi proposed a simplified model similar to the Hénon map in 1978 [1]. Since then, the research and application of Lozi map have not stopped [2][3][4][5][6][7][8][9][10][11][12][13][14]. The existence of a chaotic saddle in the Lozi Map was proved by Lopesino, et al [11].…”

Section: Introductionmentioning

confidence: 99%

The stratification and invariant region of chaotic sea in an area-preserving Lozi map

2023

Preprint

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In this paper, we study the hierarchical structure of a chaotic sea and the existence condition and delimitation method of island chain for Lozi map. The regular island chains associated with elliptic periodic points in chaotic sea are investigated by the theory presented in [15]. A method for determining the boundaries of the island chain is introduced. Multiple layers of a chaotic sea are found which are dependent on initial values. A method of determining the layer boundary of chaotic sea is presented. We found that critical line plays an important role in determining the boundaries of the layer of chaotic sea. We also prove that all trajectories are symmetric with respect to the diagonal dividing line of the second and fourth quadrants.

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Section: Introductionmentioning

confidence: 99%

The stratification and invariant region of chaotic sea in an area-preserving Lozi map

2023

Preprint

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Including stochastics in Prediction-Based Control of difference systems: Stabilizing and destabilizing by noise

Braverman,

Rodkina

2024

Systems & Control Letters

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Controlling chaotic maps using next-generation reservoir computing

Kent,

Barbosa,

Gauthier

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this work, we combine nonlinear system control techniques with next-generation reservoir computing, a best-in-class machine learning approach for predicting the behavior of dynamical systems. We demonstrate the performance of the controller in a series of control tasks for the chaotic Hénon map, including controlling the system between unstable fixed points, stabilizing the system to higher order periodic orbits, and to an arbitrary desired state. We show that our controller succeeds in these tasks, requires only ten data points for training, can control the system to a desired trajectory in a single iteration, and is robust to noise and modeling error.

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On target-oriented control of Hénon and Lozi maps

Cited by 4 publications

References 39 publications

The stratification and invariant region of chaotic sea in an area-preserving Lozi map

The stratification and invariant region of chaotic sea in an area-preserving Lozi map

Including stochastics in Prediction-Based Control of difference systems: Stabilizing and destabilizing by noise

Controlling chaotic maps using next-generation reservoir computing

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