To further increase the complexity of existing chaotic systems, the work proposes the Additive Sinusoidal Chaotic System Model (ASCSM), which adds two one-dimensional sinusoidalized conventional chaotic mappings (Logistic, Sine, Fraction) to enhance the complexity of chaotic systems. First, the performance of ASCSM is proved by theoretical analysis, and the dynamic characteristics of the enhanced chaotic mapping are simulated and analyzed according to the complexity metrics (Lyapunov exponent, spectral entropy, complexity), and the results show that the enhanced chaotic mappings performs better compared to the seed chaotic mappings. Secondly, based on the digital signal processor (DSP) platform, the feasibility of implementing the model on a hardware system is verified by generating random sequences using ASCSM. Finally, in order to compare its capability with traditional chaotic mappings in image encryption using these models as XOR sequence generators for encryption algorithms. Various cryptographic evaluation metrics demonstrate that the new model has higher confidentiality in cryptographic application.