Suppressing chaos in damped driven systems by non-harmonic excitations: experimental robustness against potential\u2019s mismatches

Faustino Palmero,Ricardo Chacón

doi:10.1007/s11071-022-07329-2

Faustino Palmero, Ricardo Chacón

Open Access

https://doi.org/10.1007/s11071-022-07329-2

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Abstract

The robustness of a chaos-suppressing scenario against potential mismatches is experimentally studied through the universal model of a damped, harmonically driven two-well Duffing oscillator subject to non-harmonic chaos-suppressing excitations. We consider a second order analogous electrical circuit having an extremely simple two-well potential that differs from that of the standard two-well Duffing model, and compare the main theoretical predictions regarding the chaos-suppressing scenario from the latter with experimental results from the former. Our experimental results prove the high robustness of the chaos-suppressing scenario against potential mismatches regardless of the (constant) values of the remaining parameters. Specifically, the predictions of an inverse dependence of the regularization area in the control parameter plane on the impulse of the chaos-suppressing excitation as well as of a minimal effective amplitude of the chaos-suppressing excitation when the impulse transmitted is maximum were experimentally confirmed.

Highlights

Palmero (B)Chacón Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain impulse transmitted is maximum were experimentally confirmed
The problem of taming chaos of general systems appears in many scientific and technological fields, including neuroscience [1], solid-state lasers [2], fluids [3], and discharge plasmas [4], among many other
For each set of control parameter values, we have implemented the function V (t) by generating it numerically in a computer and Firstly, we studied the case of a pure sinusoidal excitation (η = 0) and observed both periodic and chaotic oscillations depending on the values of the parameters

Summary

Palmero (B)

Chacón Instituto de Computación Científica Avanzada (ICCAEx), Universidad de Extremadura, E-06006 Badajoz, Spain impulse transmitted is maximum were experimentally confirmed

Introduction

Theoretical approach

Chaos-suppressing excitation

Chaotic threshold from Melnikov analysis

Experimental results

Conclusion