In this paper, we study the dynamics of two recent mean-field models representing the behavior of heterogeneous all-to-all coupled quadratic integrate-and-fire neural networks. The main difference between both models is that one considers the influence of the synaptic dynamics mechanism on the macroscopic dynamics, while the other does not. The latter model can be considered the limiting case of the former. In the literature, it has been shown, without a detailed explanation, that significant changes in the dynamics occur as synaptic dynamics increases (in the studied parametric region when considering the coupling of one excitatory and one inhibitory population): chaotic behavior disappears (or it is less frequent) and bursting dynamics emerge. The existence of synaptic dynamics, which allows a delay in synaptic transmission, seems to reduce the emergence of chaotic dynamics by increasing the synaptic time constant and maintains a phase-locked state in the form of bursting dynamics in the mean-field model. In this article, we examine in depth the different dynamical behaviors that can be found in both mean-field models (spiking, bursting, and Rössler-like chaotic behaviors) and study in detail the bifurcations underlying their appearance and disappearance. Moreover, we relate the disappearance of various behaviors with the recently introduced geometric bifurcations. Thus, our analyses provide a global view of the dynamical landscape, providing insights into the role of synaptic dynamics in coupled neural populations.

The health of aero-engines is pivotal to the safe operation of aircraft. With increasing service time, the internal components of the engine will be damaged by threats from different sources, so it is necessary to regularly detect the damage inside the engine. At present, most of the detection methods of major airlines rely on the internal images of the engine obtained by manual use of a borescope to detect damage or traditional machine learning methods, which consume high levels of human and computational resources but have low efficiency. Artificial intelligence in various fields can achieve better performance than traditional methods, but to achieve the industrialization standard of Green AI, we need further research. Accordingly, we introduce a multi-layer contrastive learning method to a lightweight target detection model design, which is applied to real aero-engine borescope images of complex components to accomplish real-time damage detection. We intensively conduct comparative experiments to evaluate the effectiveness of our method. The verification results demonstrate that the method can help our model perform excellently compared with other available baseline models.