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Suppression of chaos by incommensurate excitations: Theory and experimental confirmations

机译:通过不相称的激励抑制混沌:理论和实验验证

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We experimentally, numerically, and theoretically characterize the effectiveness of incommensurate excitations at suppressing chaos in damped driven systems. Specifically, we consider an inertial Brownian particle moving in a prototypical two-well potential and subjected to a primary (chaos-inducing) harmonic excitation and a suppressory incommensurategeneric (non-harmonic) excitation. We show that the effective amplitude of the suppressory excitation is minimal when the impulse transmitted by it is near its maximum, while its value is rather insensitive to higher-order convergents of the irrational ratio between the involved driving periods. Remarkably, the number and values of the effective initial phase difference between the two excitations are independent of the impulse while they critically depend on each particular convergent in a complex way involving both the approximate frustration of chaos-inducing homoclinic bifurcations and the maximum survival of relevant spatio-temporal symmetries of the dynamical equation. (C) 2019 Published by Elsevier B.V.
机译:我们通过实验,数值和理论上的方法来表征不相称的激励在抑制阻尼驱动系统中的混沌方面的有效性。具体而言,我们考虑惯性布朗粒子在典型的两阱势中运动,并受到一次(混沌感应)谐波激励和抑制性非对称泛型(非谐波)激励。我们显示出,抑制激励的有效振幅在其所传递的脉冲接近其最大值时是最小的,而其值对所涉及的驱动周期之间的非理性比的高次收敛并不敏感。值得注意的是,两次激发之间的有效初始相位差的数量和值与脉冲无关,而它们以复杂的方式严重依赖于每个特定的会聚点,其中包括引起混沌的同向分叉的近似受挫和相关脉冲的最大存活。动力学方程的时空对称性。 (C)2019由Elsevier B.V.发布

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