| In this thesis, we study the chaotic behavior of a fractional-order (FO) nonlinear dynamic system referred to as Jerk equation in the literature。 Our goal is not only to testify the conjecture that W.M. Ahmad and J.C. Sprott addressed in the document[4]─The third order chaotic autonomous nonlinear system with the appropriate nonlinearity and control parameters is chaotic for any fractional-order 2+ε,ε∈(0,1) , but to study in detail the ergodicity of the chaotic behavior for the Jerk equation with respect to differential order variation as well. Thus we change these parameters and let the total order () of the Jerk equation? be varied from 2.7 to 3.3, by using this approach, through computer simulations we found that the chaotic behavior of the Jerk equation can be realized provided the control parameters a, b, and c are properly chosen. Our simulation experiment results confirms the observation—the chaotic behavior of Jerk equation exhibits the ergodicity with respect to the differentiation order variation in an interval of (3-ε<<3-ε) ,where ε∈(0,1).The issue on generality of this observation is of both academic and technologic significance. The topic might be investigated through experimental study on other nonlinear dynamic systems on the one hand, and by the theoretical proof on the other hand. The later issue seems to be a great challenge to the scientists especially the mathematicians.
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