Analysis and Application of Chaotic System with Polynomial Absolute Valued Function
In order to get more complex dynamical properties,a chaotic system with cubic polyno-mial taking absolute value function is designed.The theoretical model of the chaotic system is de-scribed by a set of nonlinear equations with three state variables.The basic properties and the dy-namic characteristics of the system like phase diagram,time domain waveform,Lyapunov expo-nent,Poincaré map and bifurcation diagram are analyzed.Under certain parameter conditions,the system has periodic and chaotic properties,and there are coexistence attractors or aggregation attractors when the initial values are symmetrical.In addition,when some system parameters change,the system has constant dynamic characteristics,when the initial value of the state varia-ble changes,the dynamic characteristics of the system also remain unchanged.The correctness of the theory is verified by circuit simulation.Based on the newly designed chaotic system,an en-cryption scheme is designed,and the encryption performance is analyzed,which shows the effec-tiveness of the encryption scheme.
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