arXiv 2408.040242024-08-07nlin.CDphysics.comp-ph

使用ICO学习对非线性系统中的同步进行分类

Classification of synchronization in nonlinear systems using ICO learning

J. P. Deka

备注：: 6 pages, 5 figures

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AI总结：

本文研究输入相关性（ICO）学习在宇称-时间对称耦合Duffing振子系统同步分类中的应用，发现反相同步时权重保持恒定而准周期去同步时权重不稳定演化，证明ICO学习可用于非线性系统同步动力学分类。

摘要：

在这项工作中，我们研究了被称为输入相关性（ICO）学习的差分Hebbian学习规则在耦合非线性振子系统同步分类中的意义。我们研究的是具有非线性耗散/放大的宇称-时间对称耦合Duffing振子系统。在对该系统时间动力学的研究中，观察到系统表现出混沌以及准周期动力学。进一步研究发现，混沌动力学是畸变的反相同步，而准周期动力学是去同步的。因此，在这两种参数区域中应用ICO学习时，我们观察到当振子反相同步时，与刺激相关的权重保持不变，尽管同步中存在畸变。但当振子表现出准周期动力学时，权重随时间的演化是不稳定的。因此，由此可以确定，ICO学习可以用于非线性系统中同步动力学的分类。

英文摘要：

In this work, we investigate the implications of the differential Hebbian learning rule known as Input-Correlations (ICO) learning in the classification of synchronization in coupled nonlinear oscillator systems. We are investigating the parity-time symmetric coupled Duffing oscillator system with nonlinear dissipation/amplification. In our investigation of the temporal dynamics of this system, it is observed that the system exhibits chaotic as well as quasiperiodic dynamics. On further investigation, it is found that the chaotic dynamics is distorted anti-phase synchronized, whereas the quasiperiodic dynamics is desynchronized. So, on the application of the ICO learning in these two parametric regimes, we observe that the weight associated with the stimulus remains constant when the oscillators are anti-phase synchronized, in spite of there being distortion in the synchronization. But when the oscillators exhibit quasiperiodic dynamics, there is erratic evolution of the weight with time. So, from this, it could be ascertained that the ICO learning could be made use of in the classification of synchronization dynamics in nonlinear systems.

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