Modeling Of The Strengthened Discrete Chaotic System And Its DSP Implementation

The research of strengthened discrete chaotic system brings higher security to the practical application of chaos,and it is one of the hot topics in the field of nonlinear.In this thesis,the modeling schemes of discrete chaotic system are proposed based on perturbation control,cycloid principle and variable fractional-order operator.It lays a model and experimental foundation for the application of the discrete chaotic system.Based on the internal perturbation model,an enhanced discrete chaotic system is proposed based on perturbation control.The suitable perturbation functions are designed.By introducing internal perturbation into high-dimensional maps with Sine terms,the new models of enhanced discrete chaotic maps are obtained.The dynamical behaviors of the new maps and the original maps are analyzed by numerical simulation.The results show that the randomness,Lyapunov value and fuzzy entropy complexity of the new maps are significantly improved.Based on the principle of cycloid,a cycloid chaotic map is proposed by adopting the coupling and disturbance control method.By means of the attractor phase diagram,bifurcation diagram,Lyapunov exponents and spectral entropy complexity,the dynamical characteristics of the map with parameter changes are analyzed.The experimental results show that the attractor shape of the cycloid chaotic map is extremely sensitive to the parameters,and has rich dynamical behaviors,such as infinitely many equilibrium points,symmetric coexisting attractors,and large-scale hyperchaotic states and high complexity.Combining the fractional-order difference theory defined by Caputo with the short-memory model,the strengthened discrete chaotic system is proposed based on variable fractional-order operator.Using the variableorder functions to set as the system different orders,and the variable fractional-order Sine map is designed.The dynamical behavior of the system is analyzed by using phase diagram,time series,bifurcation diagram,Lyapunov exponents and spectral entropy complexity algorithm.The numerical simulation results show that the variable fractional-order model not only improves the chaotic parameter space and complexity value of the system,but also generates the extreme multi-stable phenomenon with infinite coexisting attractors.The randomness,security and anti-predictability of the chaotic sequences generated by the enhanced discrete chaotic systems are tested by NIST test and IRM parameter estimation algorithm,and its physical realizability and application prospect in the field of information security are verified by DSP technology.