Chaos, as an important subject of nonlinear science, plays an important role in solving problems in both natural sciences and social sciences such as the fields of secure communications, fluid motion, particle motion and so on. Aiming at this problem, this paper proposes a nonlinear dynamic system composed of product trigonometric functions and studies its chaotic characteristics. Through the mathematical derivation of the system’s period, the analysis of the necessary conditions at the fixed point, the experimental drawing of the Lyapunov exponential graph and the branch graph of the system, it is proved that the system has larger chaotic interval and stronger chaotic characteristics. The parameters of the proposed dynamic system are generated randomly, and then the chaotic sequence can be generated. The chaotic sequence is used to encrypt the digital image, a good encryption effect is obtained, and there is a large key space. At the same time, the motion of the particles in the space magnetic field is simulated, which further proves that the trigonometric system has strong chaotic characteristics.
Three-Element Problem of Carleman Type for Bianalitic Functions in a Circle
