A study on the complexity of a business cycle model with great excitements in non-resonant condition

Based on the researches of Szydlowski and Krawiec, we studied the inherent complexity of a chaotic business cycle with great excitements in non-resonant condition. First, we got the first-order and second-order approximate solutions of the system by using multiple scale method. Then deduced the formulation reflecting the complex relations between vibration, phase, bifurcation parameter μ and excite frequency Ω of first-order solution. As the great excitement F varied, the global changes of the system solutions were analyzed. We also explored the different paths leading the systems with different parameter combinations into catastrophe region, fuzzy region or chaos region. Finally, we discussed the evolution trends of business cycle models under the above-mentioned conditions. Hence, this paper has some theoretical and practical significance.