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In perturbation methods, the perturbed system is expressed as a combination of the baseline structure and the related perturbations.
If it has smoothly connected homoclinic orbits, then it cannot stand the perturbation, and its perturbed system probably produces chaotic phenomena.
For small perturbations, the eigenvalues and eigenvectors of the perturbed system can be expanded into a Taylor series.
One can notably distinguish absolute robustness, quantifying the average performance of a perturbed system, from relative robustness, quantifying performance degradation/improvement due to perturbations.
A perturbation particle representing a flux difference is explicitly transported in the perturbed system, instead of in the unperturbed system.
If we increase strength of the periodic perturbation and consider (f_0=1) with the same values of other parameters, then the perturbed system (24) shows chaotic motions.
and its perturbed system (3.28).
associated with the perturbed system.
Consider the following perturbed system: (3.10).
For every we consider the perturbed system.
we deduce that any solution of the perturbed system (1.6).
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