Lin Lifeng, Wang Huiqi
School of Big Data, Fuzhou University of International Studies and Trade, Fuzhou, 350202, China.
College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China.
Sci Rep. 2025 Jan 17;15(1):2335. doi: 10.1038/s41598-025-86080-1.
In this study, we introduce a coupled fractional system consisting of two fluctuating-mass oscillators with time delay and investigate their collective resonant behaviors. First, we achieve complete synchronization between the average behaviors of these oscillators. We then derive the exact analytical expression for the output amplitude gain, and based on this, we observe generalized stochastic resonance (GSR) in the system. We further examine how GSR behavior depends on system parameters, demonstrating that coupling strength, fractional order, and time delay are crucial in facilitating and optimizing its intensity. Finally, numerical simulations are conducted to validate the analytical results.
在本研究中，我们引入了一个由两个具有时间延迟的变质量振子组成的耦合分数阶系统，并研究它们的集体共振行为。首先，我们实现了这些振子平均行为之间的完全同步。然后，我们推导出输出幅度增益的精确解析表达式，并在此基础上，观察到系统中的广义随机共振（GSR）。我们进一步研究了GSR行为如何依赖于系统参数，表明耦合强度、分数阶和时间延迟对于促进和优化其强度至关重要。最后，进行了数值模拟以验证解析结果。
