This paper proposes a facial expression recognition network called the Lightweight Facial Network with Spatial Bias (LFNSB). The LFNSB model effectively balances model complexity and recognition accuracy. It has two key components: a lightweight feature extraction network (LFN) and a Spatial Bias (SB) module for aggregating global information. The LFN introduces combined channel operations and depth-wise convolution techniques, effectively reducing the number of parameters while enhancing feature representation capability. The Spatial Bias module enables the model to focus on local facial features while capturing the dependencies between different facial regions. Additionally, a new loss function called Cosine-Harmony Loss is designed. This function optimizes the relative positions of feature vectors in high-dimensional space, resulting in better feature separation and clustering. Experimental results on the AffectNet and RAF-DB datasets demonstrate that the LFNSB model achieves competitive recognition accuracy, with 63.12% accuracy on AffectNet-8, 66.57% accuracy on AffectNet-7, and 91.07% accuracy on RAF-DB, while significantly reducing the model complexity.

This paper proposes a novel facial expression recognition network called the Lightweight Facial Network with Spatial Bias (LFNSB). The LFNSB model balances model complexity and recognition accuracy. It has two key components: a lightweight feature extraction network (LFN) and a Spatial Bias (SB) module for aggregating global information. The LFN introduces combined channel operations and depthwise convolution techniques, effectively reducing the number of parameters while enhancing feature representation capability. The Spatial Bias module enables the model to focus on local facial features while also capturing the dependencies between different facial regions. Additionally, a novel loss function called Cosine-Harmony Loss is designed. This function optimizes the relative positions of feature vectors in high-dimensional space, resulting in better feature separation and clustering. Experimental results on the AffectNet and RAF-DB datasets show that the proposed LFNSB model performs excellently in facial expression recognition tasks. It achieves high recognition accuracy while significantly reducing the number of parameters, thus substantially lowering model complexity.

Magnetically coupled resonant wireless power transfer (MCR‐WPT) system with constant power load (CPL), finds extensive applications in military, industrial, and medical treatment. However, this system can easily exhibit complex non‐linear behaviors under certain parameter conditions due to the influences of constant power loads, switching devices, and feedback controllers. These behaviors limit the effectiveness of controllers and reduce the efficiency and stability of the system. It is necessary to study the non‐linear characteristics of the MCR‐WPT system with CPL. The stroboscopic discrete mapping of the MCR‐WPT system with CPL is established. Then the system's non‐linear dynamics are analyzed theoretically using a bifurcation diagram, the maximal Floquet multipliers, and the maximal Lyapunov exponent spectrum obtained from the proposed discrete mapping. The results show that the MCR‐WPT system with CPL will exhibit rich non‐linear dynamics with the variation of the power of CPL, such as cyclic fold bifurcation, Neimark–Scaker bifurcation, border collision bifurcations, chaos, etc. The excellent alignment of experimental and theoretical outcomes in corresponding states confirms the accuracy of the proposed discrete mapping and the nonlinear analysis of the system. The results of this study can provide a reference for selecting parameters for an actual MCR‐WPT system with CPL.

PT symmetry-based wireless power transfer (WPT) systems can achieve nearly constant output power and transfer efficiency within a coupling region, but their practical implementation is limited by strict parameter matching and poor adaptability to unequal load losses. To overcome these limitations, this paper proposes a global quasi-PT symmetric modeling method for a single-transmitter, dual-constant-power receiver WPT system. Unlike classical PT-symmetric models that impose strict symmetry on individual receiver branches, the proposed model treats the entire secondary side as an equivalent subsystem. Therefore, quasi-PT symmetry is established by approximately balancing the total secondary loss with the primary gain, rather than by enforcing identical branch losses. Based on this global model, the frequency-splitting behavior is analyzed, the strong-coupling condition is derived, and the permissible ranges of the quality factor and inductance are obtained. Theoretical calculations show that the allowable ranges of both $Q$ and $L$ under quasi-PT symmetry are approximately three times wider than those under classical PT symmetry, significantly reducing the requirement for parameter precision. Further analysis demonstrates that, under global quasi-PT symmetric strong coupling, the system can maintain near constant efficiency even when the two receiver branches have unequal losses. This relaxes the conventional constraint of precisely matched receiver losses and improves the flexibility of multi-load WPT operation. In addition, for the secondary coplanar coils, the transition from far-field coupling to near-field coupling is investigated, and a boundary-distance formula is derived. When the distance between the secondary coils is smaller than this boundary distance, the influence of cross-coupling on power distribution is further analyzed, providing guidance for receiver coil layout optimization. Experimental results verify the proposed theoretical model and analysis. The proposed global quasi-PT-symmetric method improves parameter tolerance, supports unequal receiver losses, and offers a practical design framework for robust multi-load WPT systems under variable operating conditions.