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Updated: Jul 23, 2025

Generating Strictly Controlled Stimuli for Figure Recognition Experiments
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非线性异常点在动力学上有完整的基础

Kai Bai1, Jia-Zheng Li1, Tian-Rui Liu1

  • 1Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education and School of Physics and Technology, Wuhan University, Wuhan 430072, China.

Physical review letters
|July 14, 2023
PubMed
概括

研究人员证明,合共振器中的非线性异常点 (NEP) 保持了自身基础的完整性,与传统的异常点 (EP) 不同. 这一发现解决了噪声放大问题,并使微型应用成为可能.

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Linear Approximation in Time Domain

Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
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Root loci often diverge as system poles shift from the real axis to the complex plane. Key points in this transition are the breakaway and break-in points, indicating where the root locus leaves and reenters the real axis. The branches of the root locus form an angle of 180/n degrees with the real axis, where n is the number of branches at a breakaway or break-in point.
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