This investigation examines a kicked-driven model that incorporates a distinct perturbation potential. Specifically, the kick rotor model portrays a rotor that moves freely and experiences periodic perturbations in the form of a delta function potential at discrete time intervals, which can be implemented in a pulsed laser field cold atom system. Conventionally, the perturbation potential in the kick rotor model is cosine theta. However, this research utilizes a perturbation potential of cosine squared theta. As a result, the Hamiltonian of the model is expressed as H(t) = (p^2/2m) + Kcos^2(theta) * sum(delta(t-nT)) from n = negative infinity to positive infinity, where K denotes the kick's intensity, and T represents the delta function's period.


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