Asthmatic patients suffer episodic attacks of breathing difficulty and cough. Cough sounds may be used to distinguish asthma from other lung conditions or normal, especially in the acute period. We aimed to develop a novel architecture using lightweight, handcrafted components that could still extract meaningful features. Cough sounds were recorded using mobile phones from 1428 asthmatic and healthy subjects. As cough sounds behave similarly to random noises, we used a global chaotic logistic pattern (GCLP) as a kernel for feature generation based on its ability to detect random relations among input signal values. Further, each cough sound was preprocessed to remove speech and silent periods before undergoing signal decomposition using tunable Q wavelet transformation (TQWT). The latter enabled downstream GCLP-based feature generation at multiple levels, which yielded four final feature vectors (which corresponded to the four types of TQWT-generated wavelet subbands), each of length 3584. Four feature selectors were applied to the latter, generating 16 selected feature vectors, each of length 256. A standard shallow cubic support vector machine was deployed to calculate 16 prediction vectors, which were collectively input to a mode-based iterative hard majority voting function to generate additional 15-voted results. Finally, a greedy algorithm automatically chose the best overall result, which made the model self-organized. Our model attained 99.44% classification accuracy for the collected dataset. Furthermore, our model obtained an accuracy of 98.53% with leave-one- subject-out cross-validation (LOSO CV) strategy, which justifies the robustness of the developed model.