Based on the stability theory of fractional-order systems, a projective synchronization scheme with different coefficients is realized in [Formula: see text] complex networks to build a model for fractal pattern recognition. In the proposed complex function projection synchronization scheme, first a drive-response network is constructed with [Formula: see text] fractional-order complex nodes; And then reasonable controllers are designed to realize the function projection synchronization with different projection coefficients, which are used to encode the fractal pattern; Finally, using the synchronization error system, the input variables for identifying fractal patterns can be solved, and the fractal pattern can be recognized. From the perspective of neurodynamics, the proposed model provides a better understanding of human perception system.

中文翻译：

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分数阶复杂网络中的复函数投影同步及其在分形模式识别中的应用

基于分数阶系统的稳定性理论，在[公式：见正文]复杂网络中实现不同系数的射影同步方案，建立分形模式识别模型。在所提出的复函数投影同步方案中，首先用[公式：见正文]分数阶复节点构建驱动-响应网络；然后设计合理的控制器，实现不同投影系数的函数投影同步，用于对分形图案进行编码；最后，利用同步误差系统，可以求解识别分形图案的输入变量，从而识别分形图案。从神经动力学的角度来看，所提出的模型提供了对人类感知系统的更好理解。