On Fuzzy Sine Chaotic Based Model in Security Communications

Abstract

In the fuzzy chaos based dynamical model a sine chaotic map is proposed, where the model works through designing the Takagi-Sugeno fuzzy model with If-Then fuzzy rules combined with discrete-time chaotic map as a seed map in continuous map. The chaotification method was applied through using a sine chaotic map and approached on the outputs of the Takagi-Sugeno fuzzy model. That applies the model on all chaotic trajectories of the premise variable. The proposed model requires the application on a two dimensional Lozi chaotic map as a discrete-time chaotic map. Appropriate parameters proposed to ensure the chaotic behavior for the Lozi map. Numerical simulations from Lozi chaotic outputs by supposed fuzzy model,  and presented after many iterations to compute the trajectory with sine map to be in closed interval [-1,1].Absolute values on a sine chaotic map ensure positive values in [0,1]. The model inherits features of chaotic maps. The results demonstrate the effectiveness of the model with initial values equal to zero, and the model could be implemented in generating the secret key in cryptosystems and secure communication.