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The disordered price competition among various agricultural business agents leads to chaos of agricultural products’ prices, which makes it difficult for customers to form stable price expectation and correct brand cognition, restricting the sales of agricultural products with regional brands. Based on the Salop circular market model with bounded rationality and delayed feedback, this paper discusses the complexity in price competition of agricultural products with regional brands. It is found that when the price adjustment speed of agricultural business agents exceeds the stability region, the pricing system of agricultural products with regional brands would appear the phenomenon of periodic bifurcation or chaos. The delayed feedback controlling mechanism of price adjustment could make the pricing system in the chaos state turn to the equilibrium state. Therefore, the price fluctuation of agricultural products with regional brands needs reasonable control from the industrial associations and government departments.