Lyapunov stability for detecting adversarial image examples

•Applying chaos theory to detect adversarial examples, following two different approaches.•Our proposed detection method is based on a novel approach, extracting Lyapunov exponents from neural network activations.•Adversarial examples are generated using 8 state-of-the-art methods, in datasets like MNIST and ImageNet.•Two additional adversarial detection methods are trained and compared.•Extensive discussion is performed in comparison to a plenty variety of detection techniques from different approaches.