This paper addresses the need for image copyright protection in the Internet of Things (IoT) by proposing a watermarking algorithm based on chaotic neural networks. The algorithm employs a three-dimensional memristive Rulkov model to select strong chaotic parameters for generating encryption sequences, combines cross-offset scrambling and Fibonacci matrix diffusion to achieve dual encryption, and embeds the watermark into the high-frequency sub-bands of the image through secondary discrete wavelet transform. Experimental data show that the watermarked images achieve an average PSNR of 47.8 dB, with the SSIM index consistently ranging between 0.9974 and 0.9990. By leveraging the sensitivity of chaotic systems to globalize the impact of local attacks, the watermark can be fully extracted even under cropping and noise interference, demonstrating the algorithm's strong concealment and attack resistance. Real-time processing is enabled through edge computing, providing a reliable copyright management solution for IoT scenarios such as drone inspections.