Abstract
A system is combined by itself and the periphery, and the periphery controls the system. The Periphery Theory describes that a system input is dependent on a system gate of the periphery, and the gate is considered as a switch which will adjust the state of the system automatically. In this research, a new logistic model with switch is created to learn how the switch adjust the system. The switch is set to close/open the gate of the system to decrease/increase the input, and it is related to the final states of the system. By comparing this new model with the original one, the switch also improve the complexity of the system, which changes the distribution of final system states, making the positions of the transition and bifurcation points occur earlier. Moreover, a new Feigenbaum constant for the new logistic model is 4.68274650, and it is totally different from the original one. In addition, a quantitative relationship between the probability of system switch and the final system states shows the protection provided by the gate to the system.
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