Abstract
The bistable potential function is divided into inner and outer sides. Inside and outside functions are both turned to the form of parabola, then symmetric parabolic potential function is constructed. Based on the Kramers escape theory, the Kramers escape ratio and SNR of different potential functions are analyzed and compared. The theoretical analysis and numerical simulation manifest that symmetric parabolic potential function is much better than other potential functions. The mechanism is explained which the symmetric parabolic potential function can enhance the noise effects from the perspective of dynamics. The strength of the noise effect is related to the functional form of the inside and outside potential function. And the inside of symmetric parabolic potential function plays a greater role.
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