<p>We propose the Deep Oscillatory Neural Network (DONN), a brain-inspired network architecture that incorporates oscillatory dynamics into learning. Unlike conventional neural networks with static internal states, DONN neurons exhibit brain-like oscillatory activity through neural Hopf oscillators operating in the complex domain. The network combines neural oscillators with traditional sigmoid and ReLU neurons, all employing complex-valued weights and activations. Input signals can be presented to oscillators in three modes: resonator, amplitude modulation, and frequency modulation. Training uses complex backpropagation to minimize the output error. We extend this approach to convolutional architectures, creating Oscillatory Convolutional Neural Networks (OCNNs). Evaluation on benchmark signal and image processing tasks demonstrates comparable or improved performance over baseline methods. Interestingly, the network exhibits emergent phenomena such as feature and temporal binding during image classification, a key characteristic of biological visual processing, and exhibit STDP (Spike Timing Dependent Plasticity) kernel when trained using Hebbain learning. These phenomena with explicit oscillatory dynamics enhance the interpretability of internal representations.</p>