Sensitivity Of Fuzzified Dynamical Systems Induced By Compact Systems

In the study of chaos,the understandings of scientists in different fields about the definition of chaos are different.The above differences almost dues to the sensitivity and instability of orbits.We summarize the research of sensitivity,strong sensitivity,asymptotic sensitivity,multi-sensitivity,syndetic sensitivity,thick sensitivity,ergodic sensitivity etc..Then,we study the relations between the various forms of sensitivity of the compact system and its g-fuzzification and draw the following conclusions:(1)The compact system is strongly sensitive if and only if its g-fuzzification is strongly sensitive.(2)That the compact system is asymptotic sensitive cannot imply that its g-fuzzification is asymptotic sensitive,and the counter-example is given.(3)If the g-fuzzification is Li-Yorke sensitive,the compact system has chaotic dependence on initial conditions.If the special subsystem of the g-fuzzification is Li-Yorke sensitive,the compact system is Li-Yorke sensitive.However,the Li-Yorke sensitivity of the compact system cannot imply it of the g-fuzzification.(4)The compact system is an isometry system if and only if the Zadeh's extension is an isometry system.