Construction And Noised Persurbed Structures Of Quasi-sine Fibonacci M-J Sets

The nonlinear theory is a new developing frontier science which researches the nonlinear phenomenons, and the main research contents are Soliton, Chaos and Fractal which build the base of the nonlinear theory. Here we will construct a new type of dynamic system which is arised by the introduction of the Fibonacci function. So, we call it Fibonacci hyperbolic dynamic system, and then we will begin the series of relative research. The main contents are as followings:Using the escape-time method, this paper researches the dynamic behaviors of the quasi-sine Fibonacci hyperbolic dynamic system and the generalized quasi-sine Fibonacci hyperbolic system. Construct the quasi-sine Fibonacci M-J sets, and do a further discuss of them. Calculate the integer fixed points and the fixed points on the complex plane with a certain precision. And then construct the Julia set of it using the escape-time method, discovering that the Julia set is fractal and it is on the x-axis symmetry. Using the conception of critical point, the quasi-sine Fibonacci function is generalized. Later the paper researches the dynamic behavior of the generalized quasi-sine Fibonacci function on critical points, and finds that the Mandelbrot set is also on the x-axis symmetry. It is discovered that there is a jumping phenomenon on the critical points.Study the quasi-sine Fibonacci J set which under the additive noise, multiplicative noise and the composing noise mixed by additive and multiplicative noises. Through combining the mathematical proof and the computer graphics method, we find the evolution rules during different nature and extent of deformation made by the noises.At last, we study the quasi-sine Fibonacci M set under the additive and multiplicative noises. Through combining the mathematical proof and the computer graphics method, we analyse how the different degree and type parameters do the effect on the quasi-sine Fibonacci M. Finally, we conclude the rules and corresponding characters, and also give the proofs.