State-of-The-Art algorithms for visual place recognition, and related visual navigation systems, can be broadly split into two categories: computer-science-oriented models including deep learning or image retrieval-based techniques with minimal biological plausibility, and neuroscience-oriented dynamical networks that model temporal properties underlying spatial navigation in the brain. In this letter, we propose a new compact and high-performing place recognition model that bridges this divide for the first time. Our approach comprises two key neural models of these categories: (1) FlyNet, a compact, sparse two-layer neural network inspired by brain architectures of fruit flies, Drosophila melanogaster, and (2) a one-dimensional continuous attractor neural network (CANN). The resulting FlyNet+CANN network incorporates the compact pattern recognition capabilities of our FlyNet model with the powerful temporal filtering capabilities of an equally compact CANN, replicating entirely in a hybrid neural implementation the functionality that yields high performance in algorithmic localization approaches like SeqSLAM. We evaluate our model, and compare it to three state-of-The-Art methods, on two benchmark real-world datasets with small viewpoint variations and extreme environmental changes-achieving 87% AUC results under day to night transitions compared to 60% for Multi-Process Fusion, 46% for LoST-X and 1% for SeqSLAM, while being 6.5, 310, and 1.5 times faster, respectively.